Hosoya and Merrifield-Simmons indices of some classes of corona of two graphs

Document Type : Research Paper


1 Islamic Azad University, Yazd branch

2 Yazd University


Let $G=(V,E)$ be a‎ ‎simple graph of order $n$ and size $m$‎. ‎An $r$-matching of $G$ is‎ ‎a set of $r$ edges of $G$ which no two of them have common vertex‎. ‎The Hosoya index $Z(G)$ of a graph $G$ is defined as the total‎ ‎number of its matchings‎. ‎An independent set of $G$ is a set of‎ ‎vertices where no two vertices are adjacent‎. ‎The‎
‎Merrifield-Simmons index of $G$ is defined as the total number of‎ ‎the independent sets of $G$‎. ‎In this paper we obtain Hosoya and‎ ‎Merrifield-Simmons indices of corona of some graphs‎.


Main Subjects

S. Alikhani and Y. H. Peng (2011). Independece roots and independece fractals of certain graphs. J. Appl. Math. Comput.. 36 (1-2), 89-100 S. Barnard and J. F. Child (1955). Higher-Algebra. Macmillan, London. H. Cheng and J. Yang (2012). Hosoya index of the corona of two graphs. South Asian J. Math.. 2 (2), 144-147 R. Frucht and F. Harary (1970). On the corona of two graphs. Aequationes Math.. 4, 322-324 I. Gutman (1988). On the Hosoya index of very large molecules. MATCH Commum. Math. Comput. Chem.. 23, 95-103 I. Gutman (1992). Independence vertex sets in some compound graphs. Publications de Institut Mathematique. 52, 5-9 I. Gutman and O. E. Polansky (1986). Mathematical Concepts in Organic Chemistry. Springer, Berlin. H. Hosoya (1971). Topological index: a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Jpn.. 44, 2332-2339 R. E. Merrifield and H. E. Simmons (1989). Topological Methods in Chemistry. Wiley, New York. H. Prodinger and R. F. Tichy (1982). Fibonacci numbers of graphs. Fibonacci Quart.. 20, 16-21 M. Sabzevaria and H. R. Maimani (2008). The Merrifield-Simmons indices and Hosoya indices of some classes of cartesian graph product. Iranian J. Math. Sci. and Inform.. 3 (1), 41-48 S. Wagner (2007). Extemal trees with respect to Hosoya index and Merrifield-Simmons index. MATCH Commun. Math. Comput. Chem.. 57, 221-233 S. Wu, J. Yang and H. Cheng (2012). Merriffeld-simmons index of the corona of two graphs. South Asian J. Math.. 2 (3), 274-278 K. Xu (2010). On the Hosoya index and the Merrifield-Simmons index of graphs with a given clique number. Appl. Math. Lett.. 23, 395-398
  • Receive Date: 12 June 2012
  • Revise Date: 30 September 2012
  • Accept Date: 04 November 2012
  • Published Online: 01 December 2012