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The Merrifield-Simmons index and Hosoya index of $$C(n, k, \lambda)$$ graphs. (English) Zbl 1255.05133
Summary: The Merrifield-Simmons index $$i(G)$$ of a graph $$G$$ is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets of $$G$$. The Hosoya index $$z(G)$$ of a graph $$G$$ is defined as the total number of independent edge subsets, that is, the total number of its matchings. By $$C(n,k,\lambda)$$ we denote the set of graphs with $$n$$ vertices, $$k$$ cycles, the length of every cycle is $$\lambda$$, and all the edges not on the cycles are pendant edges which are attached to the same vertex. In this paper, we investigate the Merrifield-Simmons index $$i(G)$$ and the Hosoya index $$z(G)$$ for a graph $$G$$ in $$C(n,k,\lambda)$$.
##### MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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