PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 52(66), pp. 5--9 (1992)
Independent vertex sets in some compound graphs
Ivan GutmanPrirodno-matematicki fakultet, Kragujevac, Yugoslavia
Abstract: Let $G$ be an $n$-vertex graph and $R_1,R_2,\dots,R_n$ distinct rooted graphs. The compound graph $G[R_1,R_2,\dots,R_n]$ is obtained by identifying the root of $R_i$ with the $i$-th vertex of $G$, $i=1,2,\dots,n$. We determine the number of independent vertex sets and the independence polynomial of $G[R_1,R_2,\dots,R_n]$. Several special cases of these results are pointed out.
Classification (MSC2000): 05C70, 05C99
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