MINIMUM COVERING GUTMAN ENERGY OF A GRAPH

The concept of a new kind of graph energy, namely, minimum covering energy, denoted by Ec(G), was introduced by Chandrashekar Adiga et.al in 2012. The Gutman energy is the sum of the absolute values of the eigenvalues obtained from the Gutman matrix. In this paper, we depict the minimum covering Gutman energy of a graph which can be defined as sum of the absolute values of the minimum covering Gutman eigenvalues obtained from the minimum covering Gutman matrix of a graph, , where . Here, is the degree of the node , is the shortest distance between the nodes & and is the minimum covering set. Further, we establish the upper and lower bounds for minimum covering Gutman energy.