IJPAM: Volume 64, No. 3 (2010)

UPPER MINUS DOMINATION NUMBER IN
K-REGULAR GRAPHS

Hongtao Zhao$^1$, Xinzhong Lu$^2$
$^{1,2}$Department of Mathematics
Zhejiang Normal University
Jinhua, 321004, P.R. CHINA
$^2$e-mail: [email protected]


Abstract.Let $G=(V,E)$ be a graph. A function $f:V(G)\rightarrow\{-1,0,1\}$ defined on the the vertices of $G$ is a minus domination function, if the sum of its function values over any closed neighborhood is at least one. The weight of a minus domination function is $\omega(f)=f(V)=\sum_{v\in V}f(v)$. The upper minus domination number of a graph $G$, denoted $\Gamma^{-}(G)$, equals the maximum weight of all the minimal minus domination functions of $G$.

Received: October 25, 2010

AMS Subject Classification: 26A33

Key Words and Phrases: minus domination, minus domination number, k-regular graph

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 3