Unicyclic家庭的局部发病率

Khilyah Munawaroh, A. I. Kristiana, E. R. Albirri, D. Dafik, R. Adawiyah
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引用次数: 1

摘要

本研究是图的局部不规则顶点着色的一个发展。基于定义,如下:\textbf{$l:V(G) \longrightarrow {\{1, 2, ..., k}\}$}称为顶点不规则k标记,\textbf{$w:V(G) \longrightarrow N$}其中\textbf{$w(u) = \varSigma_{ v \in N(u)}l(v)$}, $w$称为局部不规则顶点着色。对于$w$是一个局部不规则顶点着色的条件,如果\textit{opt$(l)$= min{使得$(li); li$,顶点标记函数},并且对于每个\textbf{$u,v\in E(G),w(u)\ne w(v)$}。色数局部不规则顶点着色用$\chi_{lis}(G)$表示。本文讨论了相关单环图的局部不规则顶点着色问题,并找到了它们的局部不规则色数的精确值,即蟋蟀图、网图、蝌蚪图、\textit{桃}图和牛图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Pewarnaan Titik Ketakteraturan Lokal pada Keluarga Graf Unicyclic
In this research is a development of local irregularity vertex coloring of graph. The based on definition, as follows: \textbf{$l:V(G) \longrightarrow {\{1, 2, ..., k}\}$} is called vertex irregular k-labelling and \textbf{$w:V(G) \longrightarrow N$} where \textbf{$w(u) = \varSigma_{ v \in N(u)}l(v)$}, $w$ is called local irregularity vertex coloring. A condition for $w$ to be a local irregularity vertex coloring, If \textit{opt$(l)$ = min\{maks$(li); li$, vertex labelling function}, and for every \textbf{$u,v\in E(G),w(u)\ne w(v)$}. The chromatic number local irregularity vertex coloring is denoted by $\chi_{lis}(G)$. In this paper, the researchers will discuss of local irregularity vertex coloring of related unicyclic graphs and we have found the exact value of their chromatic number local irregularity, namely cricket graph, net graph, tadpole graph, \textit{peach} graph, and bull graph.
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