Trivially extendable graphs
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CitationAngaleeswari, K., Sumathi, P. & Swaminathan, V. (2015). Trivially extendable graphs. TWMS Journal of Applied and Engineering Mathematics, 5(2), 307-313.
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.
SourceTWMS Journal of Applied and Engineering Mathematics
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