IJPAM: Volume 81, No. 5 (2012)

ON THE TOTAL SIGNED DOMINATION NUMBER OF $n\cdot C_{m}$

Ren Yuan$^1$, Feng Wei$^2$, Jirimutu$^3$
College of Mathematics
Inner Mongolia University for Nationalities
Tongliao, 028043, P.R. CHINA


Abstract. Let $\gamma_{s}^{*}(G)$ be the total signed domination number of $G$, $C_{m}$ denotes the cycle of length $m$, $n\cdot C_{m}$ denotes the graph obtained from any $n$ copies of $C_{m}$ which have just one common vertex. In this paper, we obtain the total signed domination number of $n\cdot C_{m}$ for any positive integer $n$ and $m$ satisfying ${m=4 ~or ~m\equiv 0(mod~5)}$.

Received: July 14, 2012

AMS Subject Classification: 05C69

Key Words and Phrases: graph, total signed domination function, total signed domination 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: 81
Issue: 5