Mixed metric dimension of some plane graphs
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Published:2023-04-29
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Volume:
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ISSN:1793-8309
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Container-title:Discrete Mathematics, Algorithms and Applications
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language:en
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Short-container-title:Discrete Math. Algorithm. Appl.
Author:
Kang Na1,
Li Zhiquan1,
Hou Lihang1,
Qu Jing1ORCID
Affiliation:
1. School of Mathematics and Science, Hebei GEO University, Shijiazhuang, 050031, P. R. China
Abstract
Let [Formula: see text] be a finite undirected simple connected graph with vertex set [Formula: see text] and edge set [Formula: see text]. A vertex [Formula: see text] resolves two elements (vertices or edges) [Formula: see text] if [Formula: see text]. A subset [Formula: see text] of vertices in [Formula: see text] is called a mixed metric generator for [Formula: see text] if every two distinct elements (vertices and edges) of [Formula: see text] are resolved by some vertices of [Formula: see text]. The minimum cardinality of a mixed metric generator for [Formula: see text] is called the mixed metric dimension and is denoted by [Formula: see text]. In this paper, we study the mixed metric dimension for the plane graph of web graph [Formula: see text] and convex polytope [Formula: see text].
Funder
National Natural Science Foundation of China
the Doctoral Scientific Research of Shijiazhuang University of Economics of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics