# IJPAM: Volume 55, No. 1 (2009)

**ON COMPUTING THE VULNERABILITY OF**

SOME GRAPHS AS AVERAGE

SOME GRAPHS AS AVERAGE

Department of Computer Engineering

Ege University

Bornova, Izmir, 35100, TURKEY

e-mail: vecdi.aytac@ege.edu.tr

Department of Mathematics

Ege University

Bornova, Izmir, 35100, TURKEY

e-mail: zeynep.odabas@ieu.edu.tr

**Abstract.**We investigate the resistance of a communication network to disruption of operation after the failure of certain stations or communication links, we use several vulnerability measures. If we think of a graph as modeling a network, the average lower independence number of a graph is one measure of graph vulnerability. For a vertex of a graph , the lower independence number of relative to is the minimum cardinality of a maximal independent set of that contains . The average lower independence number of , denoted by , is the value
. In this paper, we define and examine this parameter and consider the average lower independence number of binomial trees and middle graphs of some special graphs.

**Received: **July 20, 2009

**AMS Subject Classification: **05C99, 68R10, 05C40, 05C69 90C27, 90B18

**Key Words and Phrases: **vulnerability, connectivity, graph theory, middle graph, average lower independence number

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2009

**Volume:** 55

**Issue:** 1