The edge partition dimension of graphs

被引：0

作者：

Kuziak, Dorota ^{[1
]}

Maritz, Elizabeth ^{[2
]}

Vetrik, Tomas ^{[2
]}

Yero, Ismael G. ^{[3
]}

机构：

[1] Univ Cadiz, Dept Estat & Invest Operat, Algeciras, Spain

[2] Univ Free State, Dept Math & Appl Math, Bloemfontein, South Africa

[3] Univ Cadiz, Dept Matemat, Algeciras, Spain

来源：

DISCRETE MATHEMATICS LETTERS | 2023年 / 12卷

基金：

新加坡国家研究基金会;

关键词：

edge resolving partition; edge partition dimension; edge metric dimension; partition dimension;

D O I：

10.47443/dml.2023.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The edge metric dimension was introduced in 2018 and since then, it has been extensively studied. In this paper, we present a different way to obtain resolving structures in graphs in order to gain more insight into the study of edge resolving sets and resolving partitions. We define the edge partition dimension of a connected graph and bound it for graphs of given order and for graphs with given maximum degree. We obtain exact values of the edge partition dimension for multipartite graphs. Some relations between the edge partition dimension and partition dimension/edge metric dimension are also presented. Moreover, several open problems for further research are stated.

引用

页码：34 / 39

页数：6

共 10 条

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