Some extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index
نویسندگان
چکیده
The Hosoya index of a graph is defined as the total number of the matchings, including the empty edge set, of the graph. The Merrifield-Simmons index of a graph is defined as the total number of the independent vertex sets, including the empty vertex set, of the graph. Let U(n,∆) be the set of connected unicyclic graphs of order n with maximum degree ∆. We consider the Hosoya indices and the Merrifield-Simmons indices of graphs from U(n,∆). In this paper, we characterize the graphs in U(n,∆) with the maximal Hosoya index and the minimal Merrifield-Simmons index, respectively, and determine the corresponding indices. supported by NSFC 10671095
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