ON SOME BOUNDS OF THE MINIMUM EDGE DOMINATING ENERGY OF A GRAPH

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A.Sharmila , et. al.

Abstract

Let G be a simple graph of order n with vertex set V= {v1, v2, ..., vn} and edge set  E = {e1, e2, ..., em}. A subset  of E is called an edge dominating set of G if every edge of  E -  is adjacent to some edge in  .Any edge dominating set with minimum cardinality is called a minimum edge dominating set [2]. 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


G)= , where  =


The characteristic polynomial of is denoted by


fn (G, ρ) = det (ρI -  (G) ). 


The minimum edge dominating eigen values of a graph G are the eigen values of (G).  Minimum edge dominating energy of G is defined as


                (G) =   [12]


In this paper we have computed the Minimum Edge Dominating Energy of a graph. Its properties and bounds are discussed. All graphs considered here are simple, finite and undirected.

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How to Cite
et. al., A. , . (2021). ON SOME BOUNDS OF THE MINIMUM EDGE DOMINATING ENERGY OF A GRAPH. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(4), 1394–1399. Retrieved from https://turcomat.org/index.php/turkbilmat/article/view/1222
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Research Articles