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Line signed graph of a signed unit graph of commutative rings | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 8، شماره 2، شهریور 2023، صفحه 313-326 اصل مقاله (462.48 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27327.1234 | ||
| نویسنده | ||
| Pranjali Pranjali* | ||
| Department of Mathematics, University of Rajasthan, Jaipur, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| finite commutative rings؛ signed graph؛ unit graph | ||
| مراجع | ||
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[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). | ||
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