IJPAM: Volume 36, No. 2 (2007)

THE INTEGRITY OF DOUBLE VERTEX GRAPH
OF BINOMIAL TREES

Alpay Kirlangic$^1$, Ilknur Buyukkuscu$^2$
$^1$Department of Mathematics
Egean University
Bornova, Izmir, 35100, TURKEY
e-mail: alpay.kirlangic@ege.edu.tr
$^2$Software Developer
Vestel Electronic
Manisa, TURKEY
e-mail: ilknur.buyukkuscu@vestel.com.tr


Abstract.The stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. As the network begins losing links or nodes, eventually there is a loss in its effectiveness. The integrity of a graph $G$, $I(G)$, was introduced as a useful measure of the stability of a graph $G$ and is defined as $I(G)={\displaystyle\min_{S\subset V(G)}\{\vert S\vert+m(G-S)\}}$, where $m(G-S)$ denotes the order of a largest component of $G-S$, see [#!bes!#]. In this paper we calculate the integrity of double vertex graph of binomial trees $B_{2}$, $B_{3}$, and $B_{4}$.

Received: February 27, 2007

AMS Subject Classification: 05C40, 05C85

Key Words and Phrases: vulnerability, connectivity, integrity, binomial tree

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 2