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On the total restrained double Italian domination | ||
| Journal of Algebra and Related Topics | ||
| دوره 12، شماره 1، مهر 2024، صفحه 105-126 اصل مقاله (384.62 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2023.24056.1507 | ||
| نویسندگان | ||
| D. A. Mojdeh* ؛ M. Abdallah | ||
| Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| چکیده | ||
| A double Italian dominating (DID) function of a graph $G=(V,E)$ is a function $f: V(G)\to\{0,1,2,3\}$ having the property that for every vertex $v\in V$, $\sum_{u\in N_G[v]}f(u)\geq 3$, if $f(v)\in \{0,1\}$. A restrained double Italian dominating (RDID) function is a DID function $f$ such that the subgraph induced by the vertices with label $0$ has no isolated vertex. A total restrained double Italian dominating (TRDID) function is an RDID function $f$ such that the set $\{v\in V: f(v)> 0\}$ induces a subgraph with no isolated vertex.\\ We initiate the study of TRDID function of any graph $G$. The TRDID and RDID functions of the middle of any graph $G$ are investigated, and then, the sharp bounds for these parameters are established. Finally, for a graph $H$, we provide the minimum value of TRDID and RDID functions for corona graphs, $H \circ K_1$, $H \circ K_2$ and middle of them. | ||
| کلیدواژه‌ها | ||
| Double Italian domination؛ (total) restrained double Italian domination؛ middle graph | ||
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آمار تعداد مشاهده مقاله: 14 تعداد دریافت فایل اصل مقاله: 39 |
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