Muruganandam, R., Manikandan, R., Aruvi, M. (2018). Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs. Journal of Algorithms and Computation, 50(1), 1-28.

R. Muruganandam; R.S. Manikandan; M.Aruvi Aruvi. "Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs". Journal of Algorithms and Computation, 50, 1, 2018, 1-28.

Muruganandam, R., Manikandan, R., Aruvi, M. (2018). 'Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs', Journal of Algorithms and Computation, 50(1), pp. 1-28.

Muruganandam, R., Manikandan, R., Aruvi, M. Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs. Journal of Algorithms and Computation, 2018; 50(1): 1-28.

Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs

^{1}Department of Mathematics, Government Art College,Tiruchirappalli

^{2}Department of Mathematics, Bharathidasan University Constituent College, Lalgudi, Tiruchirappalli

^{3}Department of Mathematics, Anna University, Tiruchirappalli, India

Abstract

In $1994,$ degree distance of a graph was introduced by Dobrynin , Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative version of Gutman index of cartesian product of two connected graphs. And we compute the exact value for the cartesian product of two complete graphs. Using this result, we prove that our bound is tight. Also, we obtain the sharp upper bound for the multiplicative version of degree distance and the multiplicative version of Gutman index of strong product of connected and complete graphs. And we observe the exact value for the strong product of two complete graphs. From this, we prove that our bound is tight.