Tensor Product of the Power Graphs of Some Finite Rings

Masoumeh Soleimani, Mohammad Hassan Naderi, Ali Reza Ashrafi

DOI Number
First page
Last page


Suppose R is a ring. The multiplicative power graph P(R) of R is the graph
whose vertices are elements of R, where two distinct vertices x and y are adjacent if and only if there exists a positive integer n such that x^n = y or y^n = x. In this paper, the tensor product of the power graphs of some nite rings and also some main properties of them will be studied.


Power graph; bipartite graph; finite rings; tensor product


Power graph of a ring, tensor product, connected component, di- ameter, girth.

Full Text:



J. Abawajy, A. V. Kelarev, M. Chowdhury, Power graphs: a survey, Electronic J.

Graph Theory and Applications 1 (2013) (2) 125{147.

B. Bollabas, Graph Theory, An Introductory Course, Springer, New York, 1979.

P. J. Cameron, The Power Graph of a Finite Group, II, J. Group theory 13, (2010),


I. Chakrabarty, S. Ghosh and M. K. Sen, Undirected power graphs of semigroups,

Semigroup Forum 78 (3) (2009) 410{426.

B. Fine, Classication of nite rings of order p2, Mathematics Magazine 66 (1993)


M. Flagg, Power graphs of rings, preprint.

R. Hammack, W. Imrich, S. Klavazar, Handbook of Product Graphs, CRC Press,

Taylor and Francis Group, Second Edition, 2011.

A. V. Kelarev and S. J. Quinn, A combinatorial property and power graphs of

semigroups, Comment. Math. Univ. Carolin. 45 (1) (2004) 1-7.

A. V. Kelarev and S. J. Quinn, Directed graphs and combinatorial properties of

semigroups, J. Algebra 251 (1) (2002) 16{26.

A. V. Kelarev, S. J. Quinn and R. Smolikova, Power graphs and semigroups of

matrices, Bull. Austral. Math. Soc. 63 (2) (2001) 341{344.

A. V. Kelarev and S. J. Quinn, A combinatorial property and power graphs of

groups, Contributions to General Algebra 12 (Vienna, 1999), 229{235, Heyn, Kla-

genfurt, 2000.

A. V. Kelarev, Graph Algebras and Automata, Marcel Dekker, New York, 2003.

A. V. Kelarev, Ring Constructions and Applications, World Scientic, River Edge,

NJ, 2002.

G. R. Pourgholi, H. Youse-Azari, A. R. Ashra, The undirected power graph of

a nite group, Bull. Malays. Math. Sci. Soc. 38 (4) (2015) 1517-1525.

DOI: https://doi.org/10.22190/FUMI1901101S


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)