IJPAM: Volume 26, No. 2 (2006)

EDGE SIGNED DOMINATION NUMBERS OF
A GRAPH AND ITS COMPLEMENT

Xinzhong Lu
Department of Mathematics
Zhejiang Normal University
Jinhua, 321004, P.R. CHINA
e-mail: lvxingzhong@163.com


Abstract.Let $G$ be a finite connected simple graph with vertex set $V(G)$ and edge set $E(G)$. An edge signed domination function of $G$ is a function $f$: $E(G)\rightarrow\{-1,1\}$ such that $f[e]=\sum_{e'\in N[e]}f(e')\geq 1$ for all $e\in E(G)$, where $N[e]$ is the closed edge neighborhood of the edge $e$. The edge signed domination number $\gamma_s'(G)$ of $G$ is min{ $\sum_{e\in E(G)}f(e)\vert f$ is an edge signed domination function }. An edge signed domination function of weight $\gamma_s'(G)$, we call a $\gamma_s'$-function of $G$. Let $\overline G$ be the complement of the graph $G$. In this paper we establish upper and lower bounds on $\gamma_s'(G)+\gamma_s'(\overline G)$.

Received: November 20, 2005

AMS Subject Classification: 26A33

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 2