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Antipodal turiyam neutrosophic graphs
Graph theory, a mathematical field, investigates the relationships between entities through
vertices and edges [29]. Within this discipline, Uncertain Graph Theory emerges to model …
vertices and edges [29]. Within this discipline, Uncertain Graph Theory emerges to model …
Base size, metric dimension and other invariants of groups and graphs
The base size of a permutation group, and the metric dimension of a graph, are two of a
number of related parameters of groups, graphs, coherent configurations and association …
number of related parameters of groups, graphs, coherent configurations and association …
The local metric dimension of a graph
F Okamoto, B Phinezy, P Zhang - Mathematica Bohemica, 2010 - dml.cz
For an ordered set $ W=\{w_1, w_2,\ldots, w_k\} $ of $ k $ distinct vertices in a nontrivial
connected graph $ G $, the metric code of a vertex $ v $ of $ G $ with respect to $ W $ is the …
connected graph $ G $, the metric code of a vertex $ v $ of $ G $ with respect to $ W $ is the …
[HTML][HTML] Approximation complexity of metric dimension problem
M Hauptmann, R Schmied, C Viehmann - Journal of Discrete Algorithms, 2012 - Elsevier
We study the approximation complexity of the Metric Dimension problem in bounded
degree, dense as well as in general graphs. For the general case, we prove that the Metric …
degree, dense as well as in general graphs. For the general case, we prove that the Metric …
[HTML][HTML] The structure and metric dimension of the power graph of a finite group
M Feng, X Ma, K Wang - European Journal of Combinatorics, 2015 - Elsevier
The power graph PG of a finite group G is the graph with the vertex set G, where two distinct
vertices are adjacent if one is a power of the other. We first show that PG has a transitive …
vertices are adjacent if one is a power of the other. We first show that PG has a transitive …
Computing minimal doubly resolving sets of graphs
In this paper we consider the minimal doubly resolving sets problem (MDRSP) of graphs.
We prove that the problem is NP-hard and give its integer linear programming formulation …
We prove that the problem is NP-hard and give its integer linear programming formulation …
On the power graphs of certain finite groups
The power graph of a group Ω is a graph, whose node set is Ω and two distinct elements are
adjacent if and only if one is an integral power of the other. A metric dimension of a graph Γ …
adjacent if and only if one is an integral power of the other. A metric dimension of a graph Γ …
[HTML][HTML] Identification, location–domination and metric dimension on interval and permutation graphs. I. Bounds
We consider the problems of finding optimal identifying codes,(open) locating–dominating
sets and resolving sets of an interval or a permutation graph. In these problems, one asks to …
sets and resolving sets of an interval or a permutation graph. In these problems, one asks to …
The metric dimension of the total graph of a finite commutative ring
D Dolžan - Canadian Mathematical Bulletin, 2016 - cambridge.org
We study the total graph of a finite commutative ring. We calculate its metric dimension in the
case when the Jacobson radical of the ring is nontrivial, and we examine the metric …
case when the Jacobson radical of the ring is nontrivial, and we examine the metric …
Variable neighborhood search for metric dimension and minimal doubly resolving set problems
In this paper, two similar NP-hard optimization problems on graphs are considered: the
metric dimension problem and the problem of determining a doubly resolving set with the …
metric dimension problem and the problem of determining a doubly resolving set with the …