(untitled) (Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021)
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.