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Characterization of signed paths and cycles admitting minus dominating function | ||
Communications in Combinatorics and Optimization | ||
مقاله 16، دوره 5، شماره 1، شهریور 2020، صفحه 61-68 اصل مقاله (375.48 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2019.26661.1128 | ||
نویسندگان | ||
Mayamma Joseph* ؛ S.R. Shreyas | ||
Department of Mathematics, CHRIST (Deemed to be University), Bangalore-29, INDIA | ||
چکیده | ||
Let $G=(V,E,\sigma)$ be a finite signed graph. A function $f: V \rightarrow\{-1,0,1\}$ is a minus dominating function (MDF) of $ G $ if $f(u)+\sum_{v \in N(u)} \sigma (uv)f(v)\geq 1 $ for all $ u\in V $. In this paper we characterize signed paths and cycles admitting an MDF. | ||
کلیدواژهها | ||
Signed graphs؛ Minus domination؛ Minus Dominating Function | ||
مراجع | ||
[1] B.D. Acharya, Minus domination in signed graphs, Journal of Combinatorics, Information and System Sciences 37 (2012), 333–358.
[2] D. Cartwright and F. Harary, Structural balance: a generalization of heider’s theory., Psych. Rev. 63 (1956), no. 5, 277–293.
[3] J. Dunbar, S. Hedetniemi, M.A. Henning, and A. McRae, Minus domination in graphs, Discrete Math. 199 (1999), no. 1-3, 35–47.
[4] F. Harary, On the notion of balance of a signed graph, Mich. Math. J. 2 (1953), no. 2, 143–146. | ||
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