Geodesic
Independent Vertex Sets in Some Compound Graphs
Publications de l'Institut Mathématique, _N_S_52 (1992) no. 66, p. 5 .

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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 : 05C70 05C99 
@article{PIM_1992_N_S_52_66_a1,
     author = {Ivan Gutman},
     title = {Independent {Vertex} {Sets} in {Some} {Compound} {Graphs}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {5 },
     publisher = {mathdoc},
     volume = {_N_S_52},
     number = {66},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1992_N_S_52_66_a1/}
}
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Ivan Gutman. Independent Vertex Sets in Some Compound Graphs. Publications de l'Institut Mathématique, _N_S_52 (1992) no. 66, p. 5 . http://geodesic.mathdoc.fr/item/PIM_1992_N_S_52_66_a1/