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Muruganandam, R., Manikandan, R.S., Aruvi, M.Aruvi. (1397). Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs. , 50(1), 1-28. doi: 10.22059/jac.2018.7989
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". , 50, 1, 1397, 1-28. doi: 10.22059/jac.2018.7989
Muruganandam, R., Manikandan, R.S., Aruvi, M.Aruvi. (1397). 'Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs', , 50(1), pp. 1-28. doi: 10.22059/jac.2018.7989
Muruganandam, R., Manikandan, R.S., Aruvi, M.Aruvi. Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs. , 1397; 50(1): 1-28. doi: 10.22059/jac.2018.7989

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
مقاله 1، دوره 50، شماره 1، شهریور 2018، صفحه 1-28    اصل مقاله (294.87 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22059/jac.2018.7989
نویسندگان
R. Muruganandam1؛ R.S. Manikandan2؛ M.Aruvi Aruvi3
1Department of Mathematics, Government Art College,Tiruchirappalli
2Department of Mathematics, Bharathidasan University Constituent College, Lalgudi, Tiruchirappalli
3Department of Mathematics, Anna University, Tiruchirappalli, India
چکیده
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.
کلیدواژه‌ها
Topological indices؛ Vertex degree؛ Cartesian product and Strong product
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تعداد مشاهده مقاله: 497
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