## DEGREE PRODUCT POLYNOMIAL AND DEGREE PRODUCT ENERGY OF SPECIFIC GRAPHS

Published: 2017-01-29

Page: 94-102

HARISHCHANDRA S. RAMANE

Department of Mathematics, Karnatak University, Dharwad - 580003, Karnataka, India.

GOURAMMA A. GUDODAGI *

Department of Mathematics, Karnatak University, Dharwad - 580003, Karnataka, India

*Author to whom correspondence should be addressed.

### Abstract

Let G be a graph with a vertex set V (G) = {v1; v2,…,vn}. Let di be the degree of vertex vi in G. The degree product matrix of a graph G is defined as DP(G) = [dpij ] in which dpij = (di)(dj) if i = j and dpij = 0, otherwise. The degree product energy of graph G is defined as the sum of the absolute values of the eigenvalues of DP(G). In this paper we obtain the characteristic polynomial of the degree product matrix of some specific graphs such as regular graph, wheel, path, Windmill graphs. There by we obtain the degree product energy of these graphs.

Keywords: Degree of a vertex, degree product matrix, eigenvalues, degree product energy

#### How to Cite

RAMANE, H. S., & GUDODAGI, G. A. (2017). DEGREE PRODUCT POLYNOMIAL AND DEGREE PRODUCT ENERGY OF SPECIFIC GRAPHS. Asian Journal of Mathematics and Computer Research, 15(2), 94–102. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/730