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Independence fractals of fractal graphs | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 21، دوره 14، شماره 10، دی 2023، صفحه 239-246 اصل مقاله (497.1 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.28824.3325 | ||
| نویسندگان | ||
| Shahida A T* 1؛ Minirani S2؛ Sreeji P C1 | ||
| 1Department of Mathematics, M E S Mampad College, Malappuram, India | ||
| 2MPSTME, NMIMS University Mumbai, Mumbai, India | ||
| تاریخ دریافت: 15 اردیبهشت 1401، تاریخ بازنگری: 26 خرداد 1401، تاریخ پذیرش: 17 تیر 1401 | ||
| چکیده | ||
| For an ordered subset $W=\{w_{1}, w_{2},...,w_{k}\}$ of $V(G)$ and a vertex $v\in V$, the metric representation of $v$ with respect to $W$ is a $k$-vector, which is defined as $r(v/W)=\{d(v,w_{1}), d(v,w_{2}),...,d(v,w_{k})\}$. The set $W$ is called a resolving set for $G$ if $r(u/W)=r(v/W)$ implies that $u= v$ for all $u,v \in V(G)$. The minimum cardinality of a resolving set of $G$ is called the metric dimension of $G$. For two graphs $G$ and $H$, the lexicographic product $G \wr H$ of $H$ by $G$ is obtained from $G$ by replacing each vertex of $G$ with a copy of $H$. A graph $G$ is considered fractal if a graph $\Gamma$ exists, with at least two vertices, such as $G\simeq \Gamma \wr G$. This paper intends to discuss the fractal graph of some graphs and corresponding independence fractals. Also, compare the independent fractals of the fractal graph G, fractal factor $\Gamma$ and $\Gamma \wr G$. | ||
| کلیدواژه‌ها | ||
| Fractal graph؛ Egamorphism؛ Metric dimension؛ Metric basis؛ Resolving set؛ Independence Fractals | ||
| مراجع | ||
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