Hosoya index of unicyclic graphs with prescribed pendent vertices |
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Authors: | Hongbo Hua |
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Institution: | (1) Department of Computing Science, Huaiyin Institute of Technology, Huaian, Jiangsu, 223000, People’s Republic of China |
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Abstract: | The Hosoya index z(G) of a (molecular) graph G is defined as the total number of subsets of the edge set, in which any two edges are mutually independent, i.e., the total
number of independent-edge sets of G. By G(n, l, k) we denote the set of unicyclic graphs on n vertices with girth and pendent vertices being resp. l and k. Let be the graph obtained by identifying the center of the star S
n-l+1 with any vertex of C
l
. By we denote the graph obtained by identifying one pendent vertex of the path P
n-l-k+1 with one pendent vertex of . In this paper, we show that is the unique unicyclic graph with minimal Hosoya index among all graphs in G(n, l, k).
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Keywords: | Unicyclic graph Hosoya index permanent pendent vertex girth |
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