## Trivially Extendable Graphs

## Trivially Extendable Graphs

*K.Angaleeswari, P.Sumathi, V.Swaminathan*

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## Abstract

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≤ (β0(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 β0(G) = (n-3) and which is trivially extendable has been done. Similarly graphs with β0(G) = (n-2) is also studied for trivial extensibility.

## Keywords

Berge graph, Extensibility in graphs, Trivially extendable graphs