Minimum Injective Eccentric Dominating Energy of Graphs
Riyaz Ur Rehman A. *
PG and Research Department of Mathematics, Jamal Mohamed College (Affiliated to Bharathidasan University), Tiruchirappalli-620020, Tamil Nadu, India.
A. Mohamed Ismayil
PG and Research Department of Mathematics, Jamal Mohamed College (Affiliated to Bharathidasan University), Tiruchirappalli-620020, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
The minimum injective eccentric dominating energy of a graph is defined. The minimum injective eccentric dominating energy for star, complete and cocktail party graphs are computed. Inspired by McClelland’s bounds for energy of a graph, the upper and lower bounds of minimum injective eccentric dominating energy for star, complete and cocktail party graphs are discussed. Properties of eigenvalues of minimum injective eccentric dominating matrix for star, complete and cocktail party graphs are discussed.
Keywords: Domination, eccentric domination, injective eccentric dominating eigenvalues, minimum injective eccentric dominating set, minimum injective eccentric dominating energy