IJPAM: Volume 41, No. 4 (2007)

SIGNED TOTAL EDGE DOMINATION NUMBER
IN GRAPHS

Weiguo Wu$^1$, Zhurong Duan$^2$, Mingjing Gao$^3$
$^{1,2,3}$Department of Mathematics
Shanghai University
Shanghai, 200444, P.R. CHINA
$^1$e-mail: mikywwg@163.com


Abstract.Let $G=(V,E)$ be a connected graph with vertex set $V$ and edge set $E$. A signed total edge dominating function of $G$ is a function $f: E(G)\rightarrow \{-1,1\}$ such that $\sum_{\hat{e}\in N(e)}f(\hat{e})\ge 1$ for every $e\in E(G)$, where $N(e)$ is the edge neighborhood of an edge $e$. The signed total edge domination number $\gamma_{st}'(G)$ of $G$ is the minimum weight of a signed total edge dominating function on $G$. In this paper we present some lower bounds on the signed total edge domination number of a graph $G$ and find some exact values on $\gamma_{st}'(G)$ when $G$ is a complete graph, a complete bipartite graph, the grid $P_2\times P_k$ or the grid $P_2\times C_k$.

Received: July 1, 2007

AMS Subject Classification: 05C69

Key Words and Phrases: signed total edge domination number, signed total edge dominating function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 4