Kumar, M. Kamal Characteristic polynomial & domination energy of some special class of graphs. (English) Zbl 1307.05144 Int. J. Math. Comb. 2014, No. 1, 37-48 (2014). Summary: Representation of a set of vertices in a graph by means of a matrix was introduced by Sampath Kumar. Let \(G(V, E)\) be a graph and \(S\subseteq V\) be a set of vertices, we can represent the set \(S\) by means of a matrix as follows, in the adjacency matrix \(A(G)\) of \(G\) replace the \(a_{ii}\) element by 1 if and only if \(v_i\in S\). In this paper we define set energy and find its properties and also study the special case of set \(S\) being a dominating set and corresponding domination energy of some special class of graphs. Cited in 2 Documents MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 15A45 Miscellaneous inequalities involving matrices 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) Keywords:adjacency matrix; Smarandachely \(k\)-dominating set; dominating number; eigenvalues; energy of graph PDFBibTeX XMLCite \textit{M. K. Kumar}, Int. J. Math. Comb. 2014, No. 1, 37--48 (2014; Zbl 1307.05144)