Energy of a semigraph

Peer review under responsibility of Kalasalingam University.

Abstract

Semigraph is a generalization of graph. We introduce the concept of energy in a semigraph in two ways, one, the matrix energy $E_m$, as summation of singular values of the adjacency matrix of a semigraph, and the other, polynomial energy $E_{re}$, as energy of the characteristic polynomial of the adjacency matrix. We obtain some bounds for $E_m$ and show that $E_m$ is never a square root of an odd integer and $E_{re}$ 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

Notes

Peer review under responsibility of Kalasalingam University.