Minimum Transversal Eccentric Dominating Energy of Graphs
Riyaz Ur Rehman A. *
Department of Mathematics, Jamal Mohamed College (Autonomous) (Affiliated to Bharathidasan University), Tiruchirappalli-620020, Tamil Nadu, India.
A. Mohamed Ismayil
Department of Mathematics, Jamal Mohamed College (Autonomous) (Affiliated to Bharathidasan University), Tiruchirappalli-620020, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
For a graph G, the minimum transversal eccentric dominating energy \(\mathbb{E}\)\(\mathit{ted}\) (G) is the sum of the eigenvalues obtained from the minimum transversal eccentric dominating \(\mathit{n}\) x \(\mathit{n}\) matrix \(\mathbb{M}\)\(\mathit{ted}\) (G) = (\(\mathit{m}\)\(\mathit{ij}\)). In this paper \(\mathbb{E}\)\(\mathit{ted}\) (G) of some standard graphs are computed. Properties, upper and lower bounds for \(\mathbb{E}\)\(\mathit{ted}\) (G) are established.
Keywords: Transversal domination, eccentricity, transversal eccentric domination number, minimum transversal eccentric dominating set, eigenvalues, energy