Calculating Different Topological Indices of Von Neumann Regular Graph of Z_(p^α )
Subject Areas : Statistics
Shervin Sahebi
1
(Department of Mathematics, Islamic Azad University, Central Tehran Branch, 13185/768, Iran)
Mansoureh deldar
2
(گروه ریاضی، دانشکده علوم پایه، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران)
Keywords: دوم و سوم, شاخص رندیک, شاخص های زاگرب اول, شاخص وینر,
Abstract :
By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr(R). Topological indices are the numbers that is devoted to graphs and show some of their properties. In this paper, first we obtain the degree of vertices for a ring R and the number of edges in different special cases for the ring Z_(p^α ) (p is a prime number) and then we compute Zagreb indices of type one, two and three, Randic, Wiener, Hyper Wiener and reverse Wiener of Von Neumann graph.
[1] A. Jafari Taloukolue, Sh. Sahebi, (2018).Von Neumann regular graphs associated with rings, Discrete Mathematics, Algorithms and Applications, 10(3), to be appeared.
[2] H. Wiener. (1947). Structural determination of the paraffin boiling points, J. Amer. Chem., 69, 17-20.
[3] G.H. Fath-Tabar. (2011). Old and new Zagreb indices of graphs, Match Commun.Math. Chem., 65, 79-84.
[4] I. Gutman, N. Trinajstic. (1972). Graph theory and molecular orbitals. Total -elactron energy of alternate hydrocarbons, Chem.Phys. Lett., 17, 535-538.
[5] M.Randic. (1975). On characterization of molecular branching, J.Amer. Chem. Soc., 97, 6609-6615.
[6] D.F,Anderson, A.Badawi. (2012) Von Neumann Regular and relatedElements in Commutative Rings. Algebra Colloquium. 19, 1017-1040.
[7] A.T. Balaban, D. Mills, O. Ivanciuc, S.C. Basak. (2000). Reverse Wiener indices, Croat. Chem. Acta., 73, 923-941.
[8] D.J. Klein, I. Lukovits, I. Gutman. (1995). On the definition of the hyper-Wiener index for cycle-containing structures, J. Chem. Inf. Comput. Sci., 35, 50-52.
