C-consistent line signed graphs of Cayley signed graphs

Yadav, Tanuja; Kumar, Amit

doi:10.47974/JIM-1645

Open Access Research Article

C-consistent line signed graphs of Cayley signed graphs

^*Tanuja YadavCorresponding authoryadav.tanuja17@gmail.comDepartment of Mathematics and StatisticsBanasthali Vidyapith, Banasthali 304022, RajasthanIndiaView full profile → , Amit Kumaramitsu48@gmail.comDepartment of Mathematics and StatisticsBanasthali Vidyapith, Banasthali 304022, RajasthanIndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 33–49Vol. 26Issue 1January 2023DOI: 10.47974/JIM-1645XML

Published Online:: 31 Jan 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1645
Pages:: 33–49

Abstract

The Cayley graph, signed graph and line graph are well known in the literature. Now, our focus is to study line signed graphs of Cayley signed graphs. In this paper, we have characterized the Cayley sets and generating sets for which line signed graphs of Cayley signed graphs are canonically consistent(C-consistent).

Keywords

Cayley graph Finite group Generating set

Subject Classifications

13A1505C2205C75

References

[1] L.W. Beineke and F. Harary, Consistency in marked digraphs, J. Math. Psychol., 18(3), 260-269 (1978).
[2] A. Cayley, Desiderata and suggestions; The theory of groups: graphical representation, American Journal of Mathematics, 1(2), 174-176 (1878).
[3] E. Estrada, Degree heterogeneity of graph and network I. Interpretation and the heterogeneity paradox, Journal of Interdisciplinary Mathematics, 22(4), 503-529 (2019).
[4] E. Estrada, Degree heterogeneity of graph and network II. Comparison with other indices, Journal of Interdisciplinary Mathematics, 22(5), 711-735 (2019).
[5] F. Harary, On the notion of balance of a signed graph, Michigan Math, 2, 143-146 (1953-1954). Addendum, same journal preceding p. 1. MR 16, 733. ZM 56, 421.
[6] F. Harary, Graph Theory, Addison-Wesley Publ. Comp. Reading. MA (1969).
[7] N. Jacobson, Lectures in Abstract Algebra, East-West Press p. Ltd., New Delhi, (1951).
[8] M. Kraetzl and W.D. Wallis, Enterprise graphs and small worlds, Journal of Interdisciplinary Mathematics, 10(3), 349-362 (2007).
[9] Pranjali, A. Kumar and T. Yadav, Cayley Graphs Versus Algebraic Graphs, J. Indones. Math. Soc., 27(2), 130-136 (2021).
[10] Pranjali, A. Kumar and T. Yadav, C-consistent Cayley signed graphs, to appear.
[11] Pranjali, A. Kumar and T. Yadav, Cayley signed graphs associated with abelian groups, to appear.
[12] B. Satyanarayana, D. Srinivasulu, K. S. Prasad, Line Graphs and Quasi-total Graphs, International Journal of Computer Applications, 105, 0975-8887 (2014).
[13] D. Witte and J. A. Gallian, A survey: hamiltonian cycles in Cayley graphs, Discrete Mathematics North Holland, 51, 293-304 (1984).
[14] T. Yadav, A. Kumar and Pranjali, Line signed graphs of Cayley signed graphs, to appear.
[15] T. Zaslavsky, Characterizations of signed graphs, Graph Theory, 5(4), 401-406 (1981).

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