The Minimum Edge Dominating Energy of a Triangular Book and A Globe Graph
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Abstract
Let G be a simple graph of order n with vertex set and edge set . A subset of is called an edge dominating set of G if every edge of is adjacent to some edge in . Any edge dominating set with minimum cardinality is called a Minimum Edge Dominating set [1]. Let be a minimum edge dominating set of a graph G. The Minimum Edge Dominating matrix of G is the m x m matrix defined by
The characteristic polynomial of is denoted by
The Minimum Edge Dominating Eigen values of a graph G are the eigen values of. Minimum Edge Dominating Energy of G [13] is defined as the sum of the absolute values of the Minimum Edge Dominating Eigen values. i.e.,
In this paper we have computed the Minimum Edge Dominating Energy of a Triangular Book B(3,n) [11] and a Globe graph Gl(n) [12]. In this paper we have considered simple, finite and undirected graphs.
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