# IJPAM: Volume 37, No. 4 (2007)

**VULNERABILITY OF GENERALIZED**

PETERSEN GRAPHS VIA INVARIANTS

PETERSEN GRAPHS VIA INVARIANTS

Department of Applied Mathematics and Computer Sciences

Faculty of Science

Egean University

Bornova, Izmir, 35100, TURKEY

e-mail: [email protected]

e-mail: [email protected]

**Abstract.**Effectiveness of a network decreases if some nodes or links of it
break down any way. Thus, communication network must be
constructed to be stable as possible, not only with respect to the
initial disruption, but also with respect to the possible
reconstruction of the network. The vulnerability value of a
communications network shows the resistance of the network after
the disruption of some nodes or connection links until the
communication breakdown. In a network, as the number of nodes
belonging to sub networks changes, the vulnerability of the
network also changes and requires less vulnerability or greater
degrees of stability. If a graph is considered as a modelling
network, many graph parameters have been used to describe the
vulnerability of communications network, including connectivity,
integrity and tenacity. Several of these deal with two fundamental
questions about the resulting graph. How many vertices can still
communicate? How difficult is it to reconnect the graph?
Vulnerability numbers of a graph measure its durability respect to
break down. We consider the integrity and tenacity of generalized
Petersen graphs and the relation with its invariant.

**Received: **March 17, 2007

**AMS Subject Classification: **26A33

**Key Words and Phrases: **graph theory, combinatorial optimization, network connectivity, network stability, communication networks

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

**ISSN:** 1311-8080

**Year:** 2007

**Volume:** 37

**Issue:** 4