The Minimum Equitable Domination Energy of a Graph
Patel Rajendra, R. Rangarajan · MyPrints@UOM (Mysore University Library) · 2015
A subset D of V is called an equitable dominating set [8] if for every v ∈ V −Dthere exists a vertex u ∈ D such that uv ∈ E(G) and |deg(u) − deg(v)| ≤ 1, where deg(u)denotes the degree of vertex u and deg(v) denotes the degree of vertex v. Recently, The minimum covering energy Ec(G)of a graph is introduced by Prof. C. Adiga, and co-authors [1]. Motivated by [1], in this paper we define energy of minimum equitable domination EED(G) of some graphs and we obtain bounds on EED(G). We also obtain the minimum equitable domination determinant of some graph G given by detED(G) = μ1μ2 . . . μn whereμ1, μ2, . . . , μn are eigenvalues of AED(G).