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Roman domination in signed graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 5، دوره 8، شماره 2، شهریور 2023، صفحه 349-358 اصل مقاله (397.51 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27438.1264 | ||
| نویسندگان | ||
| James Joseph* ؛ Mayamma Joseph | ||
| Department of Mathematics, CHRIST(Deemed to be University), Bangalore, India | ||
| چکیده | ||
| Let $S = (G,\sigma)$ be a signed graph. A function $f: V \rightarrow \{0,1,2\}$ is a Roman dominating function on $S$ if $(i)$ for each $v \in V,$ $f(N[v]) = f(v) + \sum_{u \in N(v)} \sigma(uv ) f(u) \geq 1$ and $(ii)$ for each vertex $ v $ with $ f(v) = 0 $ there exists a vertex $u \in N^+(v)$ such that $f(u) = 2.$ In this paper we initiate a study on Roman dominating function on signed graphs. We characterise the signed paths, cycles and stars that admit a Roman dominating function. | ||
| کلیدواژه‌ها | ||
| Domination؛ Dominating functions؛ Roman dominating functions | ||
| مراجع | ||
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