Access the full text.
Sign up today, get DeepDyve free for 14 days.
G. Hendry (1989)
On mean distance in certain classes of graphsNetworks, 19
I. Gutman, E. Estrada, O. Ivanciuc (1999)
Some properties of the Wiener polynomial of treesGraph Theory Notes of New York, 36
D. Rouvray (1987)
The modeling of chemical phenomena using topological indicesJournal of Computational Chemistry, 8
R. Merris (1994)
Laplacian matrices of graphs: a surveyLinear Algebra and its Applications
E. J. Farrell, J. W. Kennedy, L. V. Quintas, S. A. Wahid (1992)
Graphs with palindromic matching and characteristic polynomialsVishwa Internat. J. Graph Theory, 1
I. Gutman (1998)
BUCKLEY-TYPE RELATIONS FOR WIENER-TYPE STRUCTURE-DESCRIPTORSJournal of The Serbian Chemical Society, 63
F. Buckley, L. Superville (1981)
Proc. Third Caribbean Conference on Combinatorics and Computing
O. Mekenyan, D. Bonchev, A. Balaban (1988)
Topological indices for molecular fragments and new graph invariantsJournal of Mathematical Chemistry, 2
O. Mekenyan, S. Dimitrov, D. Bonchev (1983)
Graph—theoretical approach to the calculation of physico-chemical properties of polymersEuropean Polymer Journal, 19
O. Mekenyan, D. Bonchev, A. T. Balaban (1988)
Topological indices for molecular fragmentsJ. Math. Chem., 2
P. Hell, Xuding Zhu (2000)
The circular chromatic number of series-parallel graphsJournal of Graph Theory
I. Gutman, L. Soltés (1991)
The Range of the Wiener Index and Its Mean Isomer DegeneracyZeitschrift für Naturforschung A, 46
I. Gutman (1998)
Distance of thorny graphsPubl. Inst. Math. (Beograd), 63
B. Mohar, T. Pisanski (1988)
How to compute the Wiener index of a graphJournal of Mathematical Chemistry, 2
P. Winkler (1990)
Mean distance in a treeDiscret. Appl. Math., 27
I. Gutman, D. Rouvray (1990)
New theorem for the wiener molecular branching index of trees with perfect matchingsComput. Chem., 14
A. A. Dobrynin (1999)
Distance of iterated line graphsGraph Theory Notes of New York, 37
R. C. Entringer, D. J. Kleitman, L. A. Székely (1996)
A note on spanning trees with minimum average distanceBull. Inst. Combin. Appl., 17
O. E. Polansky, D. Bonchev (1986)
The Wiener number of graphs. I. General theory and changes due to some graph operationsComm. Math. Chem. (MATCH), 21
P. Dankelmann (1994)
Average Distance and Independence NumberDiscret. Appl. Math., 51
A. A. Dobrynin, I. Gutman, V. Jovašević (1997)
Bicyclic graphs and their line graphs having the same Wiener indexDiskret. Anal. Issled. Oper. Ser. 2, 4
I. Gutman (1993)
Calculating theWiener number: The Doyle-Graver methodJ. Serb. Chem. Soc., 58
Ernesto Estrada, N. Guevara, I. Gutman (1998)
Extension of Edge Connectivity Index. Relationships to Line Graph Indices and QSPR ApplicationsJ. Chem. Inf. Comput. Sci., 38
B. Mohar, D. Babić, N. Trinajstic (1993)
A novel definition of the Wiener index for treesJ. Chem. Inf. Comput. Sci., 33
HU T.-C. (1974)
Optimum Communication Spanning TreesSIAM J. Comput., 3
L. Soltés (1991)
Transmission in graphs: A bound and vertex removingMathematica Slovaca, 41
I. Gutman (1992)
Independent vertex palindromic graphsGraph Theory Notes of New York, 23
A. A. Dobrynin, I. Gutman (1998)
The Wiener index for trees and graphs of hexagonal systemsDiskret. Anal. Issled. Oper. Ser. 2, 5
S. Nikolic, N. Trinajstic (1995)
The Wiener Index: Development and ApplicationsCroatica Chemica Acta, 68
I. Gutman, Ernesto Estrada (1996)
Topological Indices Based on the Line Graph of the Molecular GraphJ. Chem. Inf. Comput. Sci., 36
D. Rouvray (1986)
Predicting chemistry from topology.Scientific American, 255 3
R. C. Entringer (1997)
Distance in graphs: TreesJ. Combin. Math. Combin. Comput., 24
D. H. Rouvray (1983)
Chemical Application of Topology and Graph Theory
R. Merris (1990)
The distance spectrum of a treeJ. Graph Theory, 14
Cayley (1874)
LVII. On the mathematical theory of isomersPhilosophical Magazine Series 1, 47
M. Lepovic, I. Gutman (1998)
A Collective Property of Trees and Chemical TreesJ. Chem. Inf. Comput. Sci., 38
S. Klavžar, I. Gutman, B. Mohar (1995)
Labeling of Benzenoid Systems which Reflects the Vertex-Distance RelationsJ. Chem. Inf. Comput. Sci., 35
J. W. Kennedy (1992)
Palindromic graphsGraph Theory Notes of New York, 22
C. Barefoot, R. Entringer, L. Székely (1997)
Extremal Values for Ratios of Distances in TreesDiscret. Appl. Math., 80
D. Klein, I. Gutman (1999)
Wiener-Number-Related SequencesJ. Chem. Inf. Comput. Sci., 39
D. Stevanović, I. Gutman (1999)
Hosoya polynomials of trees with up to 10 verticesColl. Sci. Papers Fac. Sci. Kragujevac, 21
I. Gutman, Y. Yeh, Shyi-Long Lee, Yeung-Long Luo (1993)
Some recent results in the theory of the Wiener number
F. Buckley (1981)
Mean distance in line graphsCongr. Numer., 32
D. Bonchev, N. Trinajstic (1977)
Information theory, distance matrix, and molecular branchingJournal of Chemical Physics, 67
Ronghua Shi (1993)
THE AVERAGE DISTANCE OF TREES
V. Chepoi, S. Klavžar (1997)
The Wiener Index and the Szeged Index of Benzenoid Systems in Linear TimeJ. Chem. Inf. Comput. Sci., 37
S. Klavžar, J. Žerovnik (1996)
Algebraic Approach to Fasciagraphs and RotagraphsDiscret. Appl. Math., 68
D. Bonchev, I. Gutman, O. E. Polansky (1987)
Parity of the distance numbers and Wiener numbers of bipartite graphsComm. Math. Chem. (MATCH), 22
J. Plesník (1984)
On the sum of all distances in a graph or digraphJ. Graph Theory, 8
R. Entringer, D. Jackson, D. Snyder (1976)
Distance in graphsCzechoslovak Mathematical Journal, 26
I. Gutman (1993)
Some properties of the Wiener polynomialGraph Theory Notes of New York, 25
I. Gutman, Shyi-Long Lee, C. Chu, Yeung-Long Luo (1994)
Chemical applications of the Laplacian spectrum of molecular graphs: Studies of the Wiener number
I. Gutman (1994)
Frequency of even and odd numbers in distance matrixes of bipartite graphsJ. Chem. Inf. Comput. Sci., 34
I. Gutman, W. Linert, I. Lukovits, Ž. Tomović (2000)
The Multiplicative Version of the Wiener IndexJournal of chemical information and computer sciences, 40 1
M. Razinger, J. Chrétien, J. Dubois (1985)
Structural selectivity of topological indexes in alkane seriesJ. Chem. Inf. Comput. Sci., 25
I. Gutman, J. H. Potgieter (1997)
Wiener index and intermolecular forcesJ. Serb. Chem. Soc., 62
G. Caporossi, P. Hansen, I. Gutman, A. Dobrynin (1999)
Trees with Palindromic Hosoya Polynomials
O. Gerstel, S. Zaks (1993)
Graph-Theoretic Concepts in Computer Science (Wiesbaden-Naurod, 1992)
B. Mohar (1991)
Eigenvalues, diameter, and mean distance in graphsGraphs and Combinatorics, 7
E. Canfield, Robert Robinson, D. Rouvray (1985)
Determination of the Wiener molecular branching index for the general treeJournal of Computational Chemistry, 6
I. Gutman (1994)
On the distance of some compound graphsUniv. Beograd Publ. Elektrotehn. Fak. Ser. Mat., 5
V. A. Skorobogatov, A. A. Dobrynin (1986)
Influence of the structural transformations of a graph on its distanceVychisl. Sistemy, 117
B. Mohar (1991)
THE LAPLACIAN SPECTRUM OF GRAPHS y
O. E. Polansky, D. Bonchev (1990)
Theory of the Wiener number of graphs. II. Transfer graphs and some of their metric propertiesComm. Math. Chem. (MATCH), 25
F. Buckley, F. Harary (1990)
Distance in graphs
I. Gutman, Ycung-Long Luo, Shyi-Long Lee (1993)
The Mean Isomer Degeneracy of the Wiener IndexJournal of The Chinese Chemical Society, 40
A. A. Dobrynin (2000)
Branchings in trees and the calculation of the Wiener index of a treeComm. Math. Chem. (MATCH), 41
B. Mohar (1991)
Graph Theory, Combinatorics, and Applications
Onn Chan, I. Gutman, T. Lam, R. Merris (1998)
Algebraic Connections between Topological IndicesJ. Chem. Inf. Comput. Sci., 38
G. Pólya (1937)
Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische VerbindungenActa Mathematica, 68
A. A. Dobrynin, V. A. Skorobogatov (1991)
Metric invariants of subgraphs of molecular graphsVychisl. Sistemy, 140
A. Cayley (1874)
On the mathematical theory of isomersPhil. Magazine, 47
H. Hosoya (1988)
On some counting polynomials in chemistryDiscret. Appl. Math., 19
David Johnson, J. Lenstra, A. Kan (1978)
The complexity of the network design problemNetworks, 8
I. Gutman (1996)
Distance of line graphsGraph Theory Notes of New York, 31
I. Gutman, W. Linert, I. Lukovits, A. Dobrynin (1997)
Trees with Extremal Hyper-Wiener Index: Mathematical Basis and Chemical ApplicationsJ. Chem. Inf. Comput. Sci., 37
A. A. Dobrynin (1994)
Graphs with palindromic Wiener polynomialsGraph Theory Notes of New York, 27
I. Lukovits (1991)
General formulas for the Wiener IndexJ. Chem. Inf. Comput. Sci., 31
Onn Chan, T. Lam, R. Merris (1997)
Wiener Number as an Immanant of the Laplacian of Molecular GraphsJ. Chem. Inf. Comput. Sci., 37
I. Gutman (1993)
A new method for the calculation of the Wiener number of acyclic moleculesJournal of Molecular Structure-theochem, 285
R. Entringer, A. Meir, J. Moon, L. Székely (1994)
On the Wiener index of trees from certain familiesAustralas. J Comb., 10
D. J. Klein, M. Randić (1993)
Resistance distanceJ. Math. Chem., 12
C. Jordan
Sur les assemblages de lignes.Journal für die reine und angewandte Mathematik (Crelles Journal), 1869
A. Graovac, T. Pisanski (1991)
On the Wiener index of a graphJournal of Mathematical Chemistry, 8
I. Gutman, Dus, Ivan Vidovic, L. Popović (1998)
Graph representation of organic molecules Cayley's plerograms vs. his kenogramsJournal of the Chemical Society, Faraday Transactions, 94
R. C. Entringer (1999)
Combinatorics, Graph Theory, and Algorithms
J. W. Moon (1996)
On the total distance between nodes in treesSystems Sci. Math. Sci., 9
I. Gutman (1997)
A PROPERTY OF THE WIENER NUMBER AND ITS MODIFICATIONSIndian journal of chemistry. Sect. A: Inorganic, physical, theoretical & analytical, 36
F. Harary, A. Schwenk (1973)
The number of caterpillarsDiscret. Math., 6
I. Gutman (1993)
A contribution to the study of palindromic graphsGraph Theory Notes of New York, 24
A. A. Dobrynin, I. Gutman (1994)
On a graph invariant related to the sum of all distances in a graphPubl. Inst. Math. (Beograd), 56
I. Gutman (1994)
Selected properties of the Schultz molecular topological indexJ. Chem. Inf. Comput. Sci., 34
I. Gutman, L. Pavlović (1997)
More on distance of line graphsGraph Theory Notes of New York, 33
M. Juvan, B. Mohar, A. Graovac, S. Klavžar, J. Žerovnik (1995)
Fast computation of the Wiener index of fasciagraphs and rotagraphsJ. Chem. Inf. Comput. Sci., 35
I. Gutman, V. Jovasevic, A. Dobrynin (1997)
Smallest graphs for which the distance of the graph is equal to the distance of its line graph, 33
R. Merris (1989)
An edge version of the matrix-tree theorem and the wiener indexLinear & Multilinear Algebra, 25
A. A. Dobrynin (1988)
Graph distance of catacondensed hexagonal polycyclic systems under its transformationsVychisl. Sistemy, 127
I. Lukovits (1993)
Frequency of even and odd numbers in distance matrixes of treesJ. Chem. Inf. Comput. Sci., 33
P. Dankelmann (1997)
Average Distance and Domination NumberDiscret. Appl. Math., 80
H. Hosoya (1971)
Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated HydrocarbonsBulletin of the Chemical Society of Japan, 44
I. Gutman, O. Polansky (1986)
Mathematical Concepts in Organic Chemistry
V. A. Skorobogatov, A. A. Dobrynin (1988)
Metric analysis of graphsComm. Math. Chem. (MATCH), 23
I. Gutman, S. Marković, Ž. Bančević (1995)
Correlation between Wiener and quasi-Wiener indices in benzenoid hydrocarbonsJ. Serb. Chem. Soc., 60
T. D. Porter (1998)
A bound involving the centroid and Wiener index of a treeUtilitas Math., 53
A. A. Dobrynin (1994)
Construction of graphs with a palindromic Wiener polynomialVychisl. Sistemy, 151
S. H. Bertz, W. F. Wright (1998)
The graph theory approach to synthetic analysis: Definition and application of molecular complexity and synthetic complexityGraph Theory Notes of New York, 35
I. Gutman, A. A. Dobrynin (1998)
The Szeged index-a success storyGraph Theory Notes of New York, 34
M. Juvan, B. Mohar, J. Žerovnik (1997)
Distance-related Invariants on PolygraphsDiscret. Appl. Math., 80
I. Gutman, Y. N. Yeh, S. L. Lee, J. C. Chen (1994)
Wiener numbers of dendrimersComm. Math. Chem. (MATCH), 30
O. Gerstel, S. Zaks (1991)
A New Characterization of Tree Medians with Applications to Distributed Algorithms
P. Dankelmann (1993)
Computing the Average Distance of an Interval GraphInf. Process. Lett., 48
I. Gutman, Y. Yeh (1995)
The sum of all distances in bipartite graphsMathematica Slovaca, 45
J. Doyle, J. Graver (1977)
Mean distance in a graphDiscret. Math., 17
H.-Y. Zhu, D. Klein, I. Lukovits (1996)
Extensions of the Wiener NumberJ. Chem. Inf. Comput. Sci., 36
B. Zelinka (1968)
Medians and peripherians of trees, 004
P. E. John (1994)
Die Berechnung des Wiener Index für einfache PolybäumeComm. Math. Chem. (MATCH), 31
Y. Yeh, I. Gutman (1994)
On the sum of all distances in composite graphsDiscret. Math., 135
D. Klein, Z. Mihalić, D. Plavsic, N. Trinajstic (1992)
Molecular topological index: a relation with the Wiener indexJ. Chem. Inf. Comput. Sci., 32
H. Wiener (1947)
Structural determination of paraffin boiling points.Journal of the American Chemical Society, 69 1
K. Burns, R. C. Entringer (1995)
Graph Theory, Combinatorics, and Algorithms: Proceedings of the Seventh International Conference on the Theory and Applications of Graphs
I. Gutman, B. Mohar (1996)
The Quasi-Wiener and the Kirchhoff Indices CoincideJ. Chem. Inf. Comput. Sci., 36
The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. The paper outlines the results known for W of trees: methods for computation of W and combinatorial expressions for W for various classes of trees, the isomorphism–discriminating power of W, connections between W and the center and centroid of a tree, as well as between W and the Laplacian eigenvalues, results on the Wiener indices of the line graphs of trees, on trees extremal w.r.t. W, and on integers which cannot be Wiener indices of trees. A few conjectures and open problems are mentioned, as well as the applications of W in chemistry, communication theory and elsewhere.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 19, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.