The Minimum Total Edge Dominating Energy of a Graph

Abstract

The minimum covering energy ‫ܧ‬ ‫)ܩ(‬ and minimum dominating energy ‫ܧ‬ ‫)ܩ(‬ of a graph are well known problems of graph theory. Motivated by the work of [1,7] and also by similar works, in this paper, we introduced minimum total edge dominating energy ‫ܧ‬ ாௗ ‫)ܩ(‬ of a Graph is introduced. Minimum total edge dominating energy of a Star Graph and complete graph is computed.

Edge Regularity on m-Bipolar Fuzzy Graph

“…Ghorai and Pal [5,6] introduced generalized m-polar fuzzy graphs and studied some isomorphic properties and density of an m-polar fuzzy graph. Banasode and Umathar [2] introduced minimum total edge dominating energy of a graph. Bera and pal [3] introduced the concept of m-polar interval-valued fuzzy graph and studied the algebraic properties like density, regularity and irregularity etc.…”

Diametral Covering Number of a Graph

“…A lucid survey due to Manlove [8] lists all of them. Precisely, the covers give rise to many famous graph parameters, viz., vertex domination, edge domination, vertex cover, edge cover, etc., [1,3,4,9,11]. The theory of domination needs no introduction.…”