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Characteristic polynomial & domination energy of some special class of graphs. (English) Zbl 1307.05144

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.

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.)
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