IJPAM: Volume 81, No. 4 (2012)

SIGNED EDGE TOTAL DOMINATION NUMBERS
OF TWO CLASSES OF GRAPHS

Hong Xia$^1$, Feng Wei$^2$, Xu Chunlei$^3$, Jirimutu$^4$
$^{1,2,3,4}$College of Mathematics
Inner Mongolia University for Nationalities
Tongliao, 028043, P.R. CHINA


Abstract. Let $\gamma_{st}^{'}(G)$ be the signed edge total domination number of a graph $G$. A fan graph $F_{1\cdot n}$, of order $n+1$, $n>0$, is obtain from a path with $n$ vertices, denoted $P_{n}$, and a single vertex which is adjacent to every vertices of $P_{n}$. Let $C_{m}$ be an $m-$cycle. The graph $n-C_{m}$, $n\geq2$ and $m\geq3$, has $n(m-1)+1$ edges and it consists of the union of $n$ copies of $C_{m}$ with precisely one common edge. In addition, the $m-$cycle have exactly two vertices in common. In this paper, we calculate the $\gamma_{st}^{'}(F_{1\cdot n})$, $n\geq 1$ and $\gamma_{st}^{'}(n-C_{m})$, $m\geq3$, $n\geq2$.

Received: May 27, 2012

AMS Subject Classification: 05C69

Key Words and Phrases: signed edge total domination function, signed edge total domination number, fan graphs $F_{1\cdot n}$, $n-C_{m}$

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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: 81
Issue: 4