Upper bounds on distance vertex irregularity strength of some families of graphs

IF 1 Q1 MATHEMATICS
S. Cichacz, Agnieszka G�rlich, Andrea Semani�ov�-Fe�ov��kov�
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引用次数: 0

Abstract

For a graph \(G\) its distance vertex irregularity strength is the smallest integer \(k\) for which one can find a labeling \(f: V(G)\to \{1, 2, \dots, k\}\) such that \[ \sum_{x\in N(v)}f(x)\neq \sum_{x\in N(u)}f(x)\] for all vertices \(u,v\) of \(G\), where \(N(v)\) is the open neighborhood of \(v\). In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.
若干图族距离顶点不规则性强度的上界
对于一个图\(G\),它的距离顶点不规则强度是最小的整数\(k\),人们可以找到一个标记\(f: V(G)\to \{1, 2, \dots, k\}\),使得\[ \sum_{x\in N(v)}f(x)\neq \sum_{x\in N(u)}f(x)\]对于\(G\)的所有顶点\(u,v\),其中\(N(v)\)是\(v\)的开放邻域。本文给出了一般图的距离顶点不规则强度的上界。并给出了超立方体和树的距离顶点不规则强度的上界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Opuscula Mathematica
Opuscula Mathematica MATHEMATICS-
CiteScore
1.70
自引率
20.00%
发文量
30
审稿时长
22 weeks
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