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ENERGY OF COMPLEMENT OF STARS | Hampiholi | Journal of the Indonesian Mathematical Society 125 347 2 PB

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J. Indones. Math. Soc.

Vol. 19, No. 1 (2013), pp. 15–21.

ENERGY OF COMPLEMENT OF STARS

P. R. Hampiholi

1

, H. B. Walikar

2

, and B. S. Durgi

3

1

Department of Master of Computer Applications,

Gogte Institute of Technology, Udyambag, Belgaum - 590008, India

prhampi@yahoo.in

2

Department of Computer Science, Karnatak University,

Dharwad - 580003, India

walikarhb@yahoo.co.in

3

Department of Mathematics, KLE College of Engineering and Technology,

Belgaum - 590008, India

durgibs@yahoo.com

Abstract. The concept of energy of a graph was put forward by I. Gutman in

(1978). The characteristic polynomial of a graphG withp vertices is defined as φ(G:λ) =det(λI−A(G), whereA(G) is the adjacency matrix ofGandI is the unit matrix. The roots of the characteristic equationφ(G :λ) = 0, denoted by λ1, λ2, . . . , λp are the eigenvalues of G. The energy E = E(G) of a graphG is

defined as

E(G) =

p X

i=1 |λi|

The graphs with large number of edges are referred as graph representation of in-organic clusters, called as cluster graphs. In this paper we obtain the characteristic polynomial and energy of class of cluster graphs which are termed as complement of stars.

Key words and Phrases: Spectra of graphs, energy of graphs, stars, cluster graphs.

2000 Mathematics Subject Classification: 05C50

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