IJPAM: Volume 75, No. 3 (2012)

UPPER MINUS TOTAL DOMINATION NUMBER
OF 6-REGULAR GRAPH

Zhenlin Li$^1$, Xinzhong Lu$^2$
Department of Mathematics
Zhejiang Normal University
Zhejiang, P.R. CHINA


Abstract. Let $\Gamma_{t}^{-}(G)$ be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a 6-regular graph G and characterize the extremal graphs attaining the bound. Thus, we partially answer an open problem by Yan, Yang and Shan.

Received: October 1, 2011

AMS Subject Classification: 05C69

Key Words and Phrases: upper minus total domination, regular graph

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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: 75
Issue: 3