06054672

j

06054672 Sheela, Y.S.Irine Kala, R. Complementary signed dominating functions in graphs. Int. J. Contemp. Math. Sci. 6, No. 37-40, 1861-1870 (2011). 2011 Hikari Ltd, Ruse EN dominating function signed dominating function complementary signed dominating function

http://www.m-hikari.com/ijcms-2011/37-40-2011/index.html

Summary: Let $G = (V, E)$ be a graph. A function $f : V \rightarrow {+1, - 1}$ is called a complementary signed dominating function of $G$ if $\sum_{u\in N [v]} f(u)\geq 1$ for every $v\in V$ with $d(v)\neq n - 1$. The weight of $f$ is defined as $w(f ) =\sum_{v\in V} f(v)$. The complementary signed domination number of $G$ is defined as $\gamma_{cs}(G) =$ min \{$w(f ) : f$ is a minimal complementary signed dominating function of $G\}$. In this paper, we determine the value of complementary signed domination number for some special class of graphs. We also determine bounds for this parameter and exhibit the sharpness of the bounds. We also characterize graphs attaining the bounds in some special classes.