Abstract
Abstract Graph energy and domination in graphs are most studied areas of graph theory. In this paper we try to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.
Highlights
All graphs considered in this paper are finite, simple and undirected
A vertex v ∈ V (G) is pendant if |N(v)| = 1 and is called supporting vertex if it is adjacent to pendant vertex
The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G
Summary
All graphs considered in this paper are finite, simple and undirected. In particular, these graphs do not have loops. The minimum cardinality of such a set D is called the domination number γ(G) of G. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G. In [25] the authors have studied the dominating matrix which is defined as : Let G = (V, E) be a graph with V (G) = {v1, v2, · · · , vn} and let D ⊆ V (G) be a minimum dominating set of G. Let G be the 5-vertex path P5, with vertices v1, v2, v3, v4, v5 and let its minimum connected dominating set be Dc = {v2, v3, v4}. The minimum connected dominating energy is EDc(T ) = 12.398.
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