Open AccessSome new general lower bounds for mixed metric dimension of graphs
Author(s) -
Milica Milivojevic-Danas,
Jozef Kratica,
Aleksandar Savić,
Zoran Lj. Maksimović
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2113275m
Subject(s) - mathematics , metric dimension , combinatorics , vertex (graph theory) , graph , dimension (graph theory) , torus , cardinality (data modeling) , upper and lower bounds , metric (unit) , discrete mathematics , chordal graph , 1 planar graph , mathematical analysis , geometry , operations management , computer science , economics , data mining
A vertex w ? V resolves two elements x, y ? V ? E if d(w,x) ? d(w,y). The mixed resolving set is a set of vertices S, S ? V if any two elements of E ? V are resolved by some element of S. The minimum cardinality of a mixed resolving set is called the mixed metric dimension of a graph G. This paper introduces three new general lower bounds for the mixed metric dimension of a graph. The exact values of mixed metric dimension for torus graph are determined using one of these lower bounds. Finally, some illustrative examples of these new lower bounds and those known in the literature are presented on a set of some well-known graphs.