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On the powers of signed graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 7، شماره 1، شهریور 2022، صفحه 45-51 اصل مقاله (405.77 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27083.1193 | ||
| نویسندگان | ||
| Shijin T V* 1؛ Germina K A2؛ Shahul Hameed K3 | ||
| 1Department of Mathematics, Research Scholar, Central University of Kerala, Kasaragod, India. | ||
| 2Department of Mathematics, Associate Professor, Central University of Kerala, Kasaragod, India | ||
| 3Department of Mathematics, Associate Professor, K M M Government Women's College, Kannur, India. | ||
| چکیده | ||
| A signed graph is an ordered pair $\Sigma=(G,\sigma),$ where $G=(V,E)$ is the underlying graph of $\Sigma$ with a signature function $\sigma:E\rightarrow \{1,-1\}$. In this article, we define the $n^{th}$ power of a signed graph and discuss some properties of these powers of signed graphs. As we can define two types of signed graphs as the power of a signed graph, necessary and sufficient conditions are given for an $n^{th}$ power of a signed graph to be unique. Also, we characterize balanced power signed graphs. | ||
| کلیدواژه‌ها | ||
| Signed graph؛ Signed distance؛ Distance compatibility؛ Power of signed graphs | ||
| مراجع | ||
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[1] J. Akiyama, H. Era, and G. Exoo, Further results on graph equations for line graphs and n-th power graphs, Discrete Math. 34 (1981), no. 3, 209–218.
[2] F. Harary, A characterization of balanced signed graphs, Mich. Math. J. 2 (1953), 143–146.
[3] K. Shahul Hameed, T.V. Shijin, P. Soorya, K.A. Germina, and T. Zaslavsky, Signed distance in signed graphs, Linear Algebra Appl. 608 (2021), 236–247.
[4] T.V. Shijin, P. Soorya, K. Shahul Hameed, and K.A. Germina, On signed distance in product of signed graphs, (2021), communicated. | ||
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