Minimum Covering Energy of Binary Labeled Graph
Pradeep G. Bhat, Sabitha D’Souza · International Journal of Mathematics and Soft Computing · 2014
Let G be a graph with vertex set V (G) and edge set X(G) and consider the set A = f0; 1g. A mapping l : V (G) o€€€! A is called binary vertex labeling of G and l(v) is called the label of the vertex v under l. In this paper we introduce a new kind of graph energy for the binary labeled graph, the minimum covering label energy Ecl(G). It depends on the underlying graph G and on its binary labeling, upper and lower bounds for Ecl(G) are established. The minimum covering label energies of complete and star graphs are computed. The characteristic polynomial of complete bipartite graph is also obtained.