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Roman domination number of signed graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 12، دوره 8، شماره 4، اسفند 2023، صفحه 759-766 اصل مقاله (340 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27733.1341 | ||
| نویسندگان | ||
| James Joseph* 1؛ MAYAMMA JOSEPH2 | ||
| 1CHRIST(Deemed to be University), Bangalore | ||
| 2CHRIST(Deemed to be University) Hosur Road Bangalore-560029 | ||
| چکیده | ||
| A function $f:V\rightarrow \{0,1,2\}$ on a signed graph $S=(G,\sigma)$ where $G = (V,E)$ is a Roman dominating function(RDF) if $f(N[v]) = f(v) + \sum_{u \in N(v)} \sigma(uv)f(u) \geq 1$ for all $v\in V$ and for each vertex $v$ with $f(v)=0$ there is a vertex $u$ in $N^+(v)$ such that $f(u) = 2$. The weight of an RDF $f$ is given by $\omega(f) =\sum_{v\in V}f(v)$ and the minimum weight among all the RDFs on $S$ is called the Roman domination number $\gamma_R(S)$. Any RDF on $S$ with the minimum weight is known as a $\gamma_R(S)$-function. In this article we obtain certain bounds for $ \gamma_{R} $ and characterise the signed graphs attaining small values for $ \gamma_R. $ | ||
| کلیدواژه‌ها | ||
| Signed graphs؛ Dominating function؛ Roman dominating function | ||
| مراجع | ||
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