scholarly journals The mixed metric dimension of flower snarks and wheels

2021 ◽  
Vol 19 (1) ◽  
pp. 629-640
Author(s):  
Milica Milivojević Danas
Keyword(s):  
Higher Dimensions ◽  
Metric Dimension ◽  
Exact Results ◽  
Graph Invariant ◽  
Mixed Metric ◽  
Special Classes

Abstract New graph invariant, which is called a mixed metric dimension, has been recently introduced. In this paper, exact results of the mixed metric dimension on two special classes of graphs are found: flower snarks J n {J}_{n} and wheels W n {W}_{n} . It is proved that the mixed metric dimension for J 5 {J}_{5} is equal to 5, while for higher dimensions it is constant and equal to 4. For W n {W}_{n} , the mixed metric dimension is not constant, but it is equal to n n when n ≥ 4 n\ge 4 , while it is equal to 4, for n = 3 n=3 .

scholarly journals Mixed metric dimension of graphs with edge disjoint cycles

2021 ◽  
Vol 300 ◽  
pp. 1-8
Author(s):  
Jelena Sedlar ◽  
Riste Škrekovski
Keyword(s):  
Metric Dimension ◽  
Edge Disjoint ◽  
Disjoint Cycles ◽  
Mixed Metric

scholarly journals Mixed metric dimension of graphs

2017 ◽  
Vol 314 ◽  
pp. 429-438 ◽  
Author(s):  
Aleksander Kelenc ◽  
Dorota Kuziak ◽  
Andrej Taranenko ◽  
Ismael G. Yero
Keyword(s):  
Metric Dimension ◽  
Mixed Metric

scholarly journals Multiset and Mixed Metric Dimension for Starphene and Zigzag-Edge Coronoid

2021 ◽  
pp. 1-15
Author(s):  
Jia-Bao Liu ◽  
Sunny Kumar Sharma ◽  
Vijay Kumar Bhat ◽  
Hassan Raza
Keyword(s):  
Metric Dimension ◽  
Zigzag Edge ◽  
Mixed Metric

scholarly journals Computing strong metric dimension of some special classes of graphs by genetic algorithms

2008 ◽  
Vol 18 (2) ◽  
pp. 143-151 ◽  
Author(s):  
Jozef Kratica ◽  
Vera Kovacevic-Vujcic ◽  
Mirjana Cangalovic
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Graph Coloring ◽  
Crew Scheduling ◽  
Metric Dimension ◽  
Hard Problem ◽  
Genetic Operators ◽  
Strong Metric Dimension ◽  
Np Hard Problem ◽  
Special Classes

In this paper we consider the NP-hard problem of determining the strong metric dimension of graphs. The problem is solved by a genetic algorithm that uses binary encoding and standard genetic operators adapted to the problem. This represents the first attempt to solve this problem heuristically. We report experimental results for the two special classes of ORLIB test instances: crew scheduling and graph coloring.

scholarly journals On Mixed Metric Dimension of Rotationally Symmetric Graphs

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 11560-11569 ◽  
Author(s):  
Hassan Raza ◽  
Jia-Bao Liu ◽  
Shaojian Qu
Keyword(s):  
Metric Dimension ◽  
Symmetric Graphs ◽  
Rotationally Symmetric ◽  
Mixed Metric

scholarly journals The Vertex-Edge Resolvability of Some Wheel-Related Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Bao-Hua Xing ◽  
Sunny Kumar Sharma ◽  
Vijay Kumar Bhat ◽  
Hassan Raza ◽  
Jia-Bao Liu
Keyword(s):  
Connected Graph ◽  
Metric Dimension ◽  
Resolving Set ◽  
Minimum Cardinality ◽  
Wheel Graph ◽  
Wheel Graphs ◽  
Metric Dimensions ◽  
Mixed Metric

A vertex w ∈ V H distinguishes (or resolves) two elements (edges or vertices) a , z ∈ V H ∪ E H if d w , a ≠ d w , z . A set W m of vertices in a nontrivial connected graph H is said to be a mixed resolving set for H if every two different elements (edges and vertices) of H are distinguished by at least one vertex of W m . The mixed resolving set with minimum cardinality in H is called the mixed metric dimension (vertex-edge resolvability) of H and denoted by m  dim H . The aim of this research is to determine the mixed metric dimension of some wheel graph subdivisions. We specifically analyze and compare the mixed metric, edge metric, and metric dimensions of the graphs obtained after the wheel graphs’ spoke, cycle, and barycentric subdivisions. We also prove that the mixed resolving sets for some of these graphs are independent.

scholarly journals Magnetization Profile in the D= 2 Semi-Infinite Ising Model and Crossover Between Ordinary and Normal Transition

1997 ◽  
Vol 11 (17) ◽  
pp. 2075-2091 ◽  
Author(s):  
Peter Czerner ◽  
Uwe Ritschel
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Short Distance ◽  
Higher Dimensions ◽  
Scaling Analysis ◽  
Exact Results ◽  
Two Dimensional ◽  
Normal Transition ◽  
Surface Magnetization ◽  
Logarithmic Dependence

We study the two-dimensional semi-infinite Ising model with a free surface at or near bulk criticality. Special attention is paid to the influence of a boundary magnetic field h1 on the surface-near regime and the crossover between the fixed points at h1=0 and h1=∞. Near the surface, a smallh1 causes a steeply increasing magnetization m(z)~z3/8 log z as the distance z increases away from the surface. By means of a phenomenological scaling analysis, this phenomenon can be related to the well-known logarithmic dependence of the surface magnetization m1 on h1. Our analysis provides a deeper understanding of the existing exact results on m(z) and relates the short-distance phenomena in d=2 to those in higher dimensions. Both the results of the scaling analysis and the exact analytic profiles are corroborated by Monte Carlo simulations.

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