Trivially extendable graphs - Angaleeswari, K; Sumathi, P; Swaminathan, V (TWMS journal of applied and engineering mathematics, 2015)
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