On Some Structural Properties of $G_{m,n}$ Graphs

  • Ivy Chakrabarty Gopalan College of Engineering and Management, Bangalore


This is the continuation of the study on an undirected graph $G_{m,n}$ where vertex set $V=I_n=\{1,2,3,\cdots,n\}$ and $a,b\in V$ are adjacent if and only if $a\neq b$ and $a+b$ is not divisible by $m$, where $m(>1)\in \mathbb{N}$. In the present paper we computed the diameter, Weiner index, degree distance, independence number of the graph $G_{m,n}$. We also studied the complement of the graph $G_{m,n}$.

Author Biography

Ivy Chakrabarty, Gopalan College of Engineering and Management, Bangalore

Department of Mathematics, Gopalan College of Engineering and Management, Bangalore-560048, India


J. Bosak, The graphs of semigroups, Theory of Graphs and Application, Academic Press, New York (1964), 119–125.

F. Budden, Cayley graphs for some well-known groups, Mathematical Gazette 69 (1985), 271–278.

I. Chakrabarty, S.Ghosh and M.K.Sen,Undirected power graphs of semigroups, Semigroup Forum78 (2009), 410-426.

I. Chakrabarty, S.Ghosh, T.K.Mukherjee and M.K.Sen, Intersection graphs of ideals of rings, Discrete Mathematics 309 (2009),


I. Chakrabarty, An undirected graph on finite subset of natural numbers, Indian Journal of Discrete Mathematics 2 (1) (2015),


A. A. Dobrynin, A. A. Kochetova, Degree distance of a graph: a degree analogue of the Weiner index, J.Chem.Inf.Comput.Sci.

(1994), 1082-1086.

D. Gray, H. Wang, Cycles, the degree distance and the Wiener index, Open Journal of Discrete Mathematics 2 (2012), 156-159.

I. Gutman,Selected properties of the Schultz molecular topological index, J.Chem.Inf.Comput.Sci.34(1994), 1087-1089.

A. V. Kelarev and S. J. Quinn, Directed graph and combinatorial properties of semigroups, J. Algebra 251 (2002), 16-26.

D. B. West, Introduction to Graph Theory, 2nd edition, Prentice Hall, Upper Saddle River, NJ, 2001.

H. Weiner, Structural Determination of Paraffin Boiling Points, Journal of the American Chemical Society 69 (1947), no. 1, 17-20.

B. Zelinka, Intersection graphs of finite abelian groups, Czech. Math. J. 25 (100) (1975), no. 2, 171–174.

Research Articles