Results 11 to 20 of about 8,830,736 (317)

Minimum weight resolving sets of grid graphs [PDF]

Discrete Mathematics, Algorithms and Applications, 2016
For a simple graph [Formula: see text] and for a pair of vertices [Formula: see text], we say that a vertex [Formula: see text] resolves [Formula: see text] and [Formula: see text] if the shortest path from [Formula: see text] to [Formula: see text] is of a different length than the shortest path from [Formula: see text] to [Formula: see text].
Andersen, Patrick, Grigorious, Cyriac, Miller, Mirka   +2 more
openaire   +3 more sources

A Study on Fuzzy Resolving Domination Sets and Their Application in Network Theory

Mathematics, 2023
Consider a simple connected fuzzy graph (FG) G and consider an ordered fuzzy subset H = {(u1, σ(u1)), (u2, σ(u2)), …(uk, σ(uk))}, |H| ≥ 2 of a fuzzy graph; then, the representation of σ − H is an ordered k-tuple with regard to H of G. If any two elements
Manimozhi Vasuki, Ramachandramoorthi Shanmugapriya, Miroslav Mahdal, Robert Cep   +3 more
doaj   +3 more sources

The Simultaneous Strong Resolving Graph and the Simultaneous Strong Metric Dimension of Graph Families [PDF]

Mathematics, 2020
We consider in this work a new approach to study the simultaneous strong metric dimension of graphs families, while introducing the simultaneous version of the strong resolving graph.
Ismael González Yero
doaj   +3 more sources

Certain Varieties of Resolving Sets of A Graph [PDF]

Journal of the Indonesian Mathematical Society, 2021
Let G=(V,E) be a simple connected graph. For each ordered subset S={s_1,s_2,...,s_k} of V and a vertex u in V, we associate a vector Gamma(u/S)=(d(u,s_1),d(u,s_2),...,d(u,s_k)) with respect to S, where d(u,v) denote the distance between u and v in G.
B. Sooryanarayana, Suma A.S., Chandrakala S.B.   +2 more
semanticscholar   +2 more sources

Maximal resolving sets in a graph

International Journal of Mathematics for Industry
Let G be a connected graph. A subset [Formula: see text] of [Formula: see text] is called a resolving set of G if the code of any vertex [Formula: see text] with respect to S is different from the code of any other vertex where code of u with respect to ...
V. Swaminathan, R. Sundareswaran
doaj   +2 more sources

Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph

Complexity, 2020
Let G be a finite, connected graph of order of, at least, 2 with vertex set VG and edge set EG. A set S of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of S.
Jia-Bao Liu, Ali Zafari
doaj   +2 more sources

All metric bases and fault-tolerant metric dimension for square of grid [PDF]

Opuscula Mathematica, 2022
For a simple connected graph \(G=(V,E)\) and an ordered subset \(W = \{w_1,w_2,\ldots, w_k\}\) of \(V\), the code of a vertex \(v\in V\), denoted by \(\mathrm{code}(v)\), with respect to \(W\) is a \(k\)-tuple \((d(v,w_1),\ldots, d(v, w_k))\), where \(d ...
Laxman Saha, Mithun Basak, Kalishankar Tiwary   +2 more
doaj   +1 more source

A bridge between the minimal doubly resolving set problem in (folded) hypercubes and the coin weighing problem [PDF]

Discrete Applied Mathematics, 2020
In this paper, we consider the minimal doubly resolving set problem in Hamming graphs, hypercubes and folded hypercubes. We prove that the minimal doubly resolving set problem in hypercubes is equivalent to the coin weighing problem.
Changhong Lu, Qingjie Ye
semanticscholar   +1 more source

Approximation for the minimum cost doubly resolving set problem

Theoretical Computer Science, 2016
Xujin Chen, Xiaodong Hu, Changjun Wang
semanticscholar   +3 more sources

Levenshtein graphs: Resolvability, automorphisms & determining sets

Discrete Mathematics, 2023
22 pages, 3 ...
Perrin E. Ruth, Manuel E. Lladser
openaire   +2 more sources