Trivially extendable graphs

Let G be a simple graph. Let k be a positive integer. G is said to be k-extendable if every independent set of cardinality k is contained in a maximum independent set of G. G is said to be trivially extendable if G is not k-extendable for 1≤k[less than or equal to]([β.sub.0](G) - 1). A well covered...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 5; no. 2; p. 307
Main Authors Angaleeswari, K, Sumathi, P, Swaminathan, V
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.07.2015
Elman Hasanoglu
Subjects
Analysis
Applied mathematics
Extensibility
Graph theory
Graphs
Integer programming
Integers
Mathematical analysis
United States
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ISSN2146-1147
2146-1147

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Summary:Let G be a simple graph. Let k be a positive integer. G is said to be k-extendable if every independent set of cardinality k is contained in a maximum independent set of G. G is said to be trivially extendable if G is not k-extendable for 1≤k[less than or equal to]([β.sub.0](G) - 1). A well covered graph is one in which every maximal independent set is maximum. Study of k-extendable graphs has been made in [7,8,9]. In this paper a study of trivially extendable graphs is made. Characterization of graphs with [β.sub.0](G) = (n - 3) and which is trivially extendable has been done. Similarly graphs with [β.sub.0](G) = (n - 2) is also studied for trivial extensibility. Keywords: Berge graph, Extensibility in graphs, Trivially extendable graphs AMS Subject Classification: 05C69
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ISSN:2146-1147
2146-1147