The Merrifield-Simmons Index and Hosoya Index ofC(n,k,λ)Graphs
نویسندگان
چکیده
منابع مشابه
Extremal Hosoya index and Merrifield-Simmons index of hexagonal spiders
For any graph G, let m(G) and i(G) be the numbers of matchings (i.e., the Hosoya index) and the number of independent sets (i.e., the Merrifield–Simmons index) of G, respectively. In this paper, we show that the linear hexagonal spider and zig-zag hexagonal spider attain the extremal values of Hosoya index and Merrifield–Simmons index, respectively. c © 2008 Elsevier B.V. All rights reserved.
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For a graph G, the Hosoya index and the Merrifield-Simmons index are defined as the total number of its matchings and the total number of its independent sets, respectively. In this paper, we characterize the structure of those graphs that minimize the Merrifield-Simmons index and those that maximize the Hosoya index in two classes of simple connected graphs with n vertices: graphs with fixed m...
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For a graph G, the Merrifield-Simmons index i(G) and the Hosoya index z(G) are defined as the total number of independent sets and the total number of matchings of the graph G, respectively. In this paper, we characterize the graphs with the maximal Merrifield-Simmons index and the minimal Hosoya index, respectively, among the bicyclic graphs on n vertices with a given girth g.
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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, λ we denote the set of graphs with n vertices, k cyc...
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We characterize the trees T with n vertices whose Hosoya index (total number of matchings) is Z(T ) > 16fn−5 resp. the trees whose Merrifield-Simmons index (total number of independent subsets) is σ(T ) < 18fn−5 + 21fn−6, where fk is the kth Fibonacci number. It turns out that all the trees satisfying the inequality are tripodes (trees with exactly three leaves) and the path in both cases. Furt...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2012
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2012/520156