Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/some-extremal-graphs-with-respect-to-permanental-sum-0P6cab9zzq
References (33)
-
Ernesto Estrada, D. Bonchev (2013)
Chemical Graph Theory -
R Chen (2004)
A note on the relations between the permanental and characteristic polynomials of coronoid hydrocarbonsMATCH Commun. Math. Comput. Chem., 51
-
R. Merris, Kenneth Rebman, W. Watkins (1981)
Permanental polynomials of graphsLinear Algebra and its Applications, 38
-
H Liang, H Tong, F Bai (2008)
Computing the permanental polynomial of $$C_{60}$$ C 60 in parallelMATCH Commun. Math. Comput. Chem., 60
-
L. Valiant (1979)
The Complexity of Computing the PermanentTheor. Comput. Sci., 8
-
GG Cash (2000)
The permanental polynomialJ. Chem. Inf. Comput. Sci., 40
-
Francesco Belardo, V. Filippis (2011)
Computing the Permanental Polynomial of a Matrix from a Combinatorial Viewpoint -
Shunyi Liu (2017)
On the bivariate permanent polynomials of graphsLinear Algebra and its Applications, 529
-
H. Deng (2010)
Wiener indices of spiro and polyphenyl hexagonal chainsMath. Comput. Model., 55
-
D Kasum, N Trinajstić, I Gutman (1981)
Chemical graph theory. III. On permanental polynomialCroat. Chem. Acta., 54
-
Wei Li (2016)
On the skew-permanental polynomials of orientation graphsDiscret. Appl. Math., 208
-
Wei Li (2016)
Graphs whose characteristic and permanental polynomials have coefficients of the same magnitudeDiscret. Math., 339
-
T Wu, H Lai (2018)
On the permantal sum of graphsAppl. Math. Comput., 331
-
M. Borowiecki, T. Jóźwiak (1983)
A note on characteristic and permanental polynomials of multigraphs -
Yu Yang, Hongbo Liu, Hua Wang, H. Fu (2015)
Subtrees of spiro and polyphenyl hexagonal chainsAppl. Math. Comput., 268
-
W Yan, F Zhang (2004)
On the permanental polynomial of some graphsJ. Math. Chem., 35
-
W. Tutte (2004)
Graph-polynomialsAdv. Appl. Math., 32
-
Xianyong Li, Xiaofan Yang, Guoping Wang, Rongwei Hu (2014)
Hosoya Polynomials of General Spiro Hexagonal ChainsFilomat, 28
-
(2009)
Six-membered ring spiro chains with extremalMerrifield–Simmons index and Hosoya index -
Kasum, N. Trinajstic, I. Gutmana (2018)
On the Permanental Polynomial -
Heng Liang, Hui Tong, F. Bai (2008)
Computing the Permanental Polynomial of C60 in Parallel -
G. Cash (2000)
Permanental Polynomials of the Smaller FullerenesJournal of chemical information and computer sciences, 40 5
-
Shuchao Li, Wei Wei (2018)
Extremal octagonal chains with respect to the coefficients sum of the permanental polynomialAppl. Math. Comput., 328
-
P. Biler, A. Witkowski (1990)
Problems in mathematical analysis -
S Xie, F Gao, X Lu, R Huang, C Wang, X Zhang, M Liu, S Deng, L Zheng (2004)
Capturing the labile Fullerene[50] as $$C_{50}Cl_{10}$$ C 50 C l 10Science, 304
-
M Borowiecki, T Jóźwiak (1982)
Computing the permanental polynomial of a multigraphDiscuss. Math., V
-
(2018)
On the permanental nullity andmatching number of graphs -
Guihua Huang, Meijun Kuang, H. Deng (2014)
The expected values of Kirchhoff indices in the random polyphenyl and spiro chainsArs Math. Contemp., 9
-
Qiang Chou, Heng Liang, F. Bai (2011)
Remarks on the Relations Between the Permanental and Characteristic Polynomials of Fullerenes -
(2006)
Parallel Algorithms for Computing Permanents and Permanental Polynomials of Sparse Matrices -
I Gutman, GG Cash (2002)
Relations between the permanental and characteristic polynomials of fullerenes and benzenoid hydrocarbonsMATCH Commun. Math. Comput. Chem., 45
-
S. Xie, F. Gao, Xin Lu, Rong-Bin Huang, Chun-ru Wang, Xu Zhang, Mai-li Liu, Shunliu Deng, Lan-Sun Zheng (2004)
Capturing the Labile Fullerene[50] as C50Cl10Science, 304
-
Heping Zhang, Wei Li (2010)
Computing the permanental polynomials of bipartite graphs by Pfaffian orientationDiscret. Appl. Math., 160
- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-018-0642-9
- Publisher site
- See Article on Publisher Site
Abstract
Let G be a graph and A(G) the adjacency matrix of G. The polynomial $$\pi (G,x)=\mathrm {per}(xI-A(G))$$ π ( G , x ) = per ( x I - A ( G ) ) is called the permanental polynomial of G, and the permanental sum of G is the summation of the absolute values of the coefficients of $$\pi (G,x)$$ π ( G , x ) . In this paper, we give some upper and lower bounds for the permanental sum among spiro hexagonal chains, and the corresponding extremal graphs are determined. Furthermore, we investigate the more general result about permanental sum. We obtain a lower bound for the permanental sum of bipartite graphs and the corresponding extremal graphs are also determined.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Jun 4, 2018