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MAXIMAL NONHAMILTONIAN GRAPHS, STABILITY AND TOTAL VERTICES

MAXIMAL NONHAMILTONIAN GRAPHS, STABILITY AND TOTAL VERTICES DEMONSTRATIO MATHEMATICAVol. XXVNo 31992Mariusz WozniakMAXIMAL NONHAMILTONIANSTABILITYAND TOTALGRAPHS,VERTICES1. TerminologyWe consider only finite undirectedgraphswithoutloopsor multiple edges. For the sake of completeness we recall somedefinitions.LetG=(V,E)the edge setbe a graph with the vertex setE=E(G). U(G)denotes the numberof G. The graph G is tough if|S|SU(G\S)(j(G\S)>1. We shall denote bya=a(G)fortheV=V(G)ofanynectivity of G. A vertexveV(G)ScVcardinalitymaximum set of independent vertices of G and byis calledandcomponentswithofaK(G) the con-totaliffvisadjacent to all remaining vertices of G.A complete graph with nverticesisdenotedbyusually. Given graphs G and H, HcG means that H is aof G, i.e.V(H)=V(G)V(H)cV(G) andE(H)cE(G).Ifattheassubgraphsametimethen H is a factor of G.The star*denotestheoperationofjoinonvertexdisjoint graphs, with the convention thatF*G*H = (F*G)u(G*H),whereudenotesthedisjoint) graphs. GuHordinaryunionof(notnecessarilystands for vertex disjoint union of thegraphs G and H.2. Some classes of graphsIn order to formulate the results, weclasses of graphs.shalldefinesome448M. W o z n i a kD e f i n i t i o n of c l a s sthree integersKA graphn1,n2,n3>GeS°iffs u c h t h a t G isthereexistobtainedfromOKOKin t h e f o l l o w i n g w a y : in e a c h g r a p h Kwe choosel2 n3ia n db bt w o d i s t i n c t v e r t http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

MAXIMAL NONHAMILTONIAN GRAPHS, STABILITY AND TOTAL VERTICES

Woźniak, Mariusz
Demonstratio Mathematica , Volume 25 (3): 10 – Jul 1, 1992
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References (4)

Publisher
de Gruyter
Copyright
© by Mariusz Woźniak
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1992-0305
Publisher site
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Abstract

DEMONSTRATIO MATHEMATICAVol. XXVNo 31992Mariusz WozniakMAXIMAL NONHAMILTONIANSTABILITYAND TOTALGRAPHS,VERTICES1. TerminologyWe consider only finite undirectedgraphswithoutloopsor multiple edges. For the sake of completeness we recall somedefinitions.LetG=(V,E)the edge setbe a graph with the vertex setE=E(G). U(G)denotes the numberof G. The graph G is tough if|S|SU(G\S)(j(G\S)>1. We shall denote bya=a(G)fortheV=V(G)ofanynectivity of G. A vertexveV(G)ScVcardinalitymaximum set of independent vertices of G and byis calledandcomponentswithofaK(G) the con-totaliffvisadjacent to all remaining vertices of G.A complete graph with nverticesisdenotedbyusually. Given graphs G and H, HcG means that H is aof G, i.e.V(H)=V(G)V(H)cV(G) andE(H)cE(G).Ifattheassubgraphsametimethen H is a factor of G.The star*denotestheoperationofjoinonvertexdisjoint graphs, with the convention thatF*G*H = (F*G)u(G*H),whereudenotesthedisjoint) graphs. GuHordinaryunionof(notnecessarilystands for vertex disjoint union of thegraphs G and H.2. Some classes of graphsIn order to formulate the results, weclasses of graphs.shalldefinesome448M. W o z n i a kD e f i n i t i o n of c l a s sthree integersKA graphn1,n2,n3>GeS°iffs u c h t h a t G isthereexistobtainedfromOKOKin t h e f o l l o w i n g w a y : in e a c h g r a p h Kwe choosel2 n3ia n db bt w o d i s t i n c t v e r t

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 1992

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