Line signed graph of a signed unit graph of commutative rings

Document Type : Original paper

Author

Department of Mathematics, University of Rajasthan, Jaipur, India

Abstract

In this paper we characterize the commutative rings with unity for which line signed graph of signed unit graph is balanced and consistent. To do this, first we derive some sufficient conditions for balance and consistency of signed unit graphs. The results have been demonstrated with ample number of examples.

Keywords

Main Subjects


[1] N. Ashrafi, H.R. Maimani, M.R. Pournaki, and S. Yassemi, Unit graphs associated with rings, Comm. Algebra 38 (2010), no. 8, 2851–2871.
[2] M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesely Publication Company, 1969.
[3] M. Behzad and G.T. Chartrand, Line coloring of signed graphs, Elem. Math. 24 (1969), no. 3, 49–52.
[4] L.W. Beineke and F. Harary, Consistency in marked digraphs, J. Math. Psychol. 18 (1978), no. 3, 260–269.
[5] F. Harary, On the notion of balance of a signed graph., Michigan Math. J. 2 (1953), no. 2, 143–146.
[6] F. Harary, Graph Theory, Addison-Wesley Publ. Comp., Reading, MA, 1969.
[7] A. Kumar, Pranjali, M. Acharya, and P. Sharma, Unit graphs having their domination number half their order, Recent Advancements in Graph Theory (P. Shrimali and N. Shah, eds.), CRC Press, New York, 2020, pp. 205–218.
[8] Pranjali and A. Kumar, Balanced signed unit graphs, (submitted).