The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs
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,...
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/520156 |
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| author | Shaojun Dai Ruihai Zhang |
| author_facet | Shaojun Dai Ruihai Zhang |
| author_sort | Shaojun Dai |
| collection | DOAJ |
| description | 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 cycles, the length of every cycle is λ, 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,λ). |
| format | Article |
| id | doaj-art-c6f7d69e2b88424582ea988aa42a1922 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c6f7d69e2b88424582ea988aa42a19222025-02-03T06:07:08ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/520156520156The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) GraphsShaojun Dai0Ruihai Zhang1Department of Mathematics, Tianjin Polytechnic University, No. 399 Binshuixi Road, Xiqing District, Tianjin 300387, ChinaDepartment of Mathematics, Tianjin University of Science and Technology, Tianjin 300457, ChinaThe 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 cycles, the length of every cycle is λ, 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,λ).http://dx.doi.org/10.1155/2012/520156 |
| spellingShingle | Shaojun Dai Ruihai Zhang The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs Journal of Applied Mathematics |
| title | The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs |
| title_full | The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs |
| title_fullStr | The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs |
| title_full_unstemmed | The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs |
| title_short | The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs |
| title_sort | merrifield simmons index and hosoya index of c n k λ graphs |
| url | http://dx.doi.org/10.1155/2012/520156 |
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