The Multiplicative Versions of The Reciprocal Degree Distance and The Reciprocal Gutman Index of Some Graph Products
Abstract
In this paper, we provide exact value of the multiplicative versionof the reciprocal degree distance and the multiplicative version of the reciprocal Gutman index of Cartesian product of complete graphs. Also, we establish sharp upper bounds for the multiplicative version of the reciprocal degree distance and multiplicative version of the reciprocal Gutman index of strong
product of graphs.
References
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[8] M.Hoji, Z.Luo and E.Vumar. Wiener and vertex PI indices of kronecker products of graphs, Dicrete Appl: Mathe:; 158(2010); 1848-1855.
[9] H.Hua and S.Zhang. On the reciprocal degree distance of graphs, Discrete Appl: Math: 160(2012); 1152-1163.
[10] M. H. Khalifeh, H. Youseri-Azari and A. R. Ashra, Vertex and edge PI indices of Cartesian product of graphs, Discrete Appl: Math:; 156 (2008); 1780-1789.
[11] K.Pattabiraman and P.Paulraja. On some topological indices of the tesor product of graphs. Discrete Appl: Math:; 160(2012); 267-279.
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[13] K.Pattabiraman. Product version of reciprocal degree distance of graphs. Bull. Inter. Math. Virtual Inst., 7(2017), 193-202.
[14] G.Su, I.Gutman, L.Xiong and L.Xu. Reciprocal product degree distance of graphs, Filomat 30(2016); 2217-2231.
[15] R.Todeschini and V.Consonni, Handbook of molecular descriptors (Wiley -VCH, Weinheim, 2000,). doi : 10:1002=9783527613106.
[16] H.Wiener structure determination of the paraffin boiling points, J:Amer: Chem: Soc; 69(1947); 17-20: doi : 1021=ja01193a005:
[17] K.Xu, K.C. Das, H.Hua and M.V. Diudea. Maximal Harary index of unicyclic graphs with given matching number, Stud:Univ:Babes - Bolyai Chem:; 58(2013); 71-86.
[18] K.Xu,J.Wang and H.Liu. The Harary index of ordinary and generalized quasi-tree graphs, J:Appl: Math: Comput: doi : 10:1007=s12190-013 - 0727 - 4:
[19] H.Youse-Azari, M.H.Khalifeh and A.R.Ashra. Calculating the edge Wiener and edge Szeged indices of graphs, J:Comput: Appl: Math:; 235(2011); 4866-4870.
[2] T.Doslic, Vertex-weighted Wiener polynomials for composite graphs, Arc Math, Contemp., 1(2008), 66-80.
[3] A.A.Dobrynin, R.Entringer and I.Gutman, Wiener index of trees: Theory and applications; Acta: Appl: Math: 66(2001); 211 - 249:
[4] A.A.Dobrynin and A.A.Kochetova, Degree Distance of a graph: a degree analogue of the Wiener index , J:Chem: Inf: Comput: Sci:; 34(1994); 1082 - 1086.
[5] J.Devillers and A.T.Balaban(Eds.). Topological indices and related descriptors in QSAR and QSPR, Gordon and Breach ; Amsterdam; The Nethelands; 1999.
[6] I.Gutman, Selected properties of the Schultz molecular topological index, J:Chem: Inf: Comput: Sci:; 34(1994); 1087 - 1089:
[7] I.Gutman and O.E.Polansky, Mathematical concepts in orgnic chemistry (Springer - verlag); Berlin; 1986.
[8] M.Hoji, Z.Luo and E.Vumar. Wiener and vertex PI indices of kronecker products of graphs, Dicrete Appl: Mathe:; 158(2010); 1848-1855.
[9] H.Hua and S.Zhang. On the reciprocal degree distance of graphs, Discrete Appl: Math: 160(2012); 1152-1163.
[10] M. H. Khalifeh, H. Youseri-Azari and A. R. Ashra, Vertex and edge PI indices of Cartesian product of graphs, Discrete Appl: Math:; 156 (2008); 1780-1789.
[11] K.Pattabiraman and P.Paulraja. On some topological indices of the tesor product of graphs. Discrete Appl: Math:; 160(2012); 267-279.
[12] K.Pattabiraman and P.Paulraja. Wiener and vertex PI indices of the strong product of graphs. Discuss: Math: Graph Theory 32(2012); 749-769.
[13] K.Pattabiraman. Product version of reciprocal degree distance of graphs. Bull. Inter. Math. Virtual Inst., 7(2017), 193-202.
[14] G.Su, I.Gutman, L.Xiong and L.Xu. Reciprocal product degree distance of graphs, Filomat 30(2016); 2217-2231.
[15] R.Todeschini and V.Consonni, Handbook of molecular descriptors (Wiley -VCH, Weinheim, 2000,). doi : 10:1002=9783527613106.
[16] H.Wiener structure determination of the paraffin boiling points, J:Amer: Chem: Soc; 69(1947); 17-20: doi : 1021=ja01193a005:
[17] K.Xu, K.C. Das, H.Hua and M.V. Diudea. Maximal Harary index of unicyclic graphs with given matching number, Stud:Univ:Babes - Bolyai Chem:; 58(2013); 71-86.
[18] K.Xu,J.Wang and H.Liu. The Harary index of ordinary and generalized quasi-tree graphs, J:Appl: Math: Comput: doi : 10:1007=s12190-013 - 0727 - 4:
[19] H.Youse-Azari, M.H.Khalifeh and A.R.Ashra. Calculating the edge Wiener and edge Szeged indices of graphs, J:Comput: Appl: Math:; 235(2011); 4866-4870.
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2017-05-14
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