Energy of a semigraph

Abstract

Semigraph is a generalization of graph. We introduce the concept of energy in a semigraph in two ways, one, the matrix energy , as summation of singular values of the adjacency matrix of a semigraph, and the other, polynomial energy , as energy of the characteristic polynomial of the adjacency matrix. We obtain some bounds for and show that is never a square root of an odd integer and cannot be an odd integer. We investigate matrix energy of a partial semigraph and change in the matrix energy due to edge deletion.

Keywords

• semigraph
• matrix energy of a semigraph
• polynomial energy of a semigraph
• edge induced complete semigraph
• edge induced complete closure