IJPAM: Volume 85, No. 4 (2013)

DOMINATION ON
LEXICOGRAPHICAL PRODUCT OF COMPLETE GRAPHS

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


Abstract. Let γ(G) and γ'(G) be the domination number and edge domination number, respectively. The lexicographical Product G1•G2 of graph of G1 and G2 has vertex set V(G1 • G2)=V(G1) × V(G2) and edge set

E(G1 • G2)={(u1v1)(u2v2) | [u1u2 ∈ E(G1)]∪[u1=u2 and v1v2 ∈ E(G2)]}.
In this paper, we determined generalization of domination and edge domination number on lexicographical product of complete graphs and any simple graph.

Received: February 9, 2013

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

Key Words and Phrases: lexicographical product, domination number, edge domination number

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DOI: 10.12732/ijpam.v85i4.10 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: 2013
Volume: 85
Issue: 4