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The Merrifield-Simmons Index and Hosoya Index of ð ¶ ( ð ‘› , 𠑘 , 𠜆 ) Graphs

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  • Shaojun Dai
  • Ruihai Zhang

Abstract

The Merrifield-Simmons index ð ‘– ( ð º ) of a graph ð º 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 ð º The Hosoya index 𠑧 ( ð º ) of a graph ð º is defined as the total number of independent edge subsets, that is, the total number of its matchings. By ð ¶ ( ð ‘› , 𠑘 , 𠜆 ) we denote the set of graphs with ð ‘› vertices, 𠑘 cycles, the length of every cycle is 𠜆 , 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 ð ‘– ( ð º ) and the Hosoya index 𠑧 ( ð º ) for a graph ð º in ð ¶ ( ð ‘› , 𠑘 , 𠜆 ) .

Suggested Citation

  • Shaojun Dai & Ruihai Zhang, 2012. "The Merrifield-Simmons Index and Hosoya Index of ð ¶ ( ð ‘› , 𠑘 , 𠜆 ) Graphs," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-8, July.
    • Handle: RePEc:hin:jnljam:520156
    DOI: 10.1155/2012/520156
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