Degree distance and Gutman index of two graph products
DOI:
https://doi.org/10.13069/jacodesmath.729422Keywords:
Degree distance, Adjacency matrix, Distance matrix, Complete product, Strong productAbstract
The degree distance was introduced by Dobrynin, Kochetova and Gutman as a weighted version of the Wiener index. In this paper, we investigate the degree distance and Gutman index of complete, and strong product graphs by using the adjacency and distance matrices of a graph.
Received: 10 August 2017 | Accepted: 15 August 2019Downloads
References
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(5) (1994) 1082–1086.
A. A. Dobrynin, R. Entringer, and I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. Math. 66(3) (2001) 211–249.
M. Eliasi and B. Taeri, Four operations on graphs and the Wiener index, Discrete Appl. Math. 157(4) (2009) 693–703.
I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34(5) (1994) 1087–1089.
I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17(4) (1972) 535–538.
I. Gutman, B. Ruščić, N. Trinajstić, and C. F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62(9) (1975) 3399–3405.
W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition, John Wiley & Sons, New York (2000).
M. H. Khalifeh, H. Yousefi-Azari, and A. R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157(4) (2009) 804–811.
M. H. Khalifeh, H. Yousefi-Azari, and A. R. Ashrafi, The hyper-Wiener index of graph operations, Discrete Appl. Math. 156(12) (2008) 2202–2207.
M. H. Khalifeh, H. Yousefi-Azari, and A. R. Ashrafi, Vertex and edge-Wiener indices of composite graphs, Discrete Appl. Math. 156(10) (2008) 1780–1789.
P. S. Ranjini, V. Lokesha, and I. Gutman, An exceptional property of the Gutman index, Front. Math. China 6(4) (2011) 745–748.
P. S. Ranjini, V. Lokesha, and M. A. Rajan, On the Zagreb indices of the subdivisions of graphs, Int. J. Contemp. Math. Sci. 6(17-20) (2011) 905–910.
H. P. Schultz, Topological organic chemistry. 1. Graph theory and topological indices of alkanes, J. Chem. Inf. Comput. Sci. 29(3) (1989) 227–228.
H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69(1) (1947) 17–20.
W. Yan and B.-Y. Yang, The Wiener index of the corona of two graphs, Discrete Appl. Math. 154(17) (2006) 2422–2431.
H. Yousefi-Azari, M. H. Khalifeh, and A. R. Ashrafi, Calculating the degree distance and Gutman index of some graph operations, Polym. Bull. 67(4) (2011) 685–693.
S. Roy and M. K. Sen, Degree distance of some graph operations, Arabian J. Math. 3(4) (2014) 211–222.
Y. N. Yeh and I. Gutman, On the sum of all distances in composite graphs, J. Comput. Chem. 15(1) (1994) 97–107.
B. Zhou and N. Trinajstić, On the Gutman index and reciprocal degree distance, Chem. Phys. Lett. 453(4-6) (2008) 293–296.
B. Zhou and N. Trinajstić, Some properties of the Gutman index, Chem. Phys. Lett. 455(1-3) (2008) 120–123.
B. Zhou and N. Trinajstić, On the degree distance and Gutman index of trees, J. Math. Chem. 47(1) (2010) 259–265.
