IJPAM: Volume 98, No. 1 (2015)

SIGNED CLIQUE EDGE-DOMATIC NUMBER OF A GRAPH

Zhang Li-Xian$^1$, Lu Xin-Zhong$^2$
$^{1,2}$Department of Mathematics
Zhejiang Normal University
Zhejiang, P.R. CHINA


Abstract. In this paper, the problem of signed clique edge-domatic number is considered for any finite,nonempty and simple graph $G$ with the maximal clique $K_{\omega}$. At first,using induction method, we study the signed clique edge-domatic number for a class of graphs with maximal clique $K_{\omega}$($\omega=2,3$). By inducing and summarizing,we obtain that the signed clique edge-domatic number on this class of graphs and the signed clique edge-domatic number of their maximal clique $K_{\omega}$ have some relations. Inspired by ways and regulars of the proof of graphs with $\omega(G)=2,3$, we take seriously to study the signed clique edge-domatic number for any graph $G$ with $K_{\omega}(\omega\geq4)$ and have proved that the signed clique edge-domatic numbers on $G$ and on $K_{\omega}(\omega\geq4)$ are equal, so we achieve the signed clique edge-domatic number for any graph $G$. This conclusion is a practical significance for the promotion of signed edge-domatic number.

Received: September 21, 2014

AMS Subject Classification: 05C69

Key Words and Phrases: clique, signed clique edge domination, signed clique edge-domatic number, signed clique edge dominating family

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DOI: 10.12732/ijpam.v98i1.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 1
Pages: 157 - 168


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