IJPAM: Volume 97, No. 3 (2014)

MATCHING AND EDGE COVERING NUMBER ON
STRONG PRODUCT OF COMPLETE BIPARTITE GRAPHS

Thanin Sitthiwirattham
Department of Mathematics
Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok, 10800, THAILAND


Abstract. Let $\alpha'(G)$ and $\beta'(G)$ be the matching and edge covering number , respectively. The strong product $G_1 \boxtimes G_2$ of graph of $G_1$ and $G_2$ has vertex set $V(G_1 \boxtimes G_2)=V(G_1)\times V(G_2)$ and edge set $E(G_1 \boxtimes G_2)=\{(u_1,v_1)(u_2,v_2)\vert[u_1u_2 \in E(G_1)$ and $v_1v_2 \in E(G_2)]$ or $[u_1=u_2$ and $v_1v_2 \in E(G_2)]$ or $[u_1u_2 \in E(G_1)$ and $v_1=v_2]\}$. In this paper, we determined generalization of matching number and edge covering number on strong product of complete bipartite graphs and any simple graph.

Received: August 28, 2014

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

Key Words and Phrases: strong product, edge covering number, matching number

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DOI: 10.12732/ijpam.v97i3.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 3
Pages: 359 - 367


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