IJPAM: Volume 77, No. 4 (2012)

VERTEX COVERING AND INDEPENDENT NUMBER
ON DIFFERENCE GRAPHS

Thanin Sitthiwirattham
Department of Mathematics
Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok, 10800, THAILAND
and
Centre of Excellence in Mathematics, CHE
Sri Ayutthaya Road, Bangkok 10400, THAILAND


Abstract. Let $\alpha(G)$ and $\beta(G)$ be the independent number and vertex covering number of G, respectively. The difference graph, $G_1\bigtriangleup G_2$, of connected graphs $G_1$ and $G_2$ has vertex set $V(G_1\bigtriangleup G_2)=V(G_1)=V(G_2)$ and edge set $E(G_1 \bigtriangleup G_2)=[E(G_1)-E(G_2)]\cup [E(G_2)-E(G_1)]$. In this paper, we determine generalizations of some graph parameters : independent number and vertex covering number on difference graph.

Received: February 28, 2012

AMS Subject Classification: 05C69, 05C70, 05C76

Key Words and Phrases: difference graph, independent number, vertex covering number

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 4