TY - JOUR

T1 - The forcing strong metric dimension of a graph

AU - Lenin, R.

AU - Kathiresan, K. M.

AU - Bača, M.

N1 - Publisher Copyright:
© 2017 University of Calgary.

PY - 2017

Y1 - 2017

N2 - For any two vertices u, v in a connected graph G, the interval I(u, v) consists of all vertices which are lying in some u − v shortest path in G. A vertex x in a graph G strongly resolves a pair of vertices u, v if either u ∈ I(x, v) or v ∈ I(x, u). A set of vertices W of V (G) is called a strong resolving set if every pair of vertices of G is strongly resolved by some vertex of W. The minimum cardinality of a strong resolving set in G is called the strong metric dimension of G and it is denoted by sdim(G). For a strong resolving set W of G, a subset S of W is called the forcing subset of W if W is the unique strong resolving set containing S. The forcing number f(W, sdim(G)) of W in G is the minimum cardinality of a forcing subset for W, while the forcing strong metric dimension, fsdim(G), of G is the smallest forcing number among all strong resolving sets of G. The forcing strong metric dimensions of some well-known graphs are determined. It is shown that for any positive integers a and b, with 0 ≤ a ≤ b, there is nontrivial connected graph G with sdim(G) = b and fsdim(G) = a if and only if {a, b} = {0, 1}.

AB - For any two vertices u, v in a connected graph G, the interval I(u, v) consists of all vertices which are lying in some u − v shortest path in G. A vertex x in a graph G strongly resolves a pair of vertices u, v if either u ∈ I(x, v) or v ∈ I(x, u). A set of vertices W of V (G) is called a strong resolving set if every pair of vertices of G is strongly resolved by some vertex of W. The minimum cardinality of a strong resolving set in G is called the strong metric dimension of G and it is denoted by sdim(G). For a strong resolving set W of G, a subset S of W is called the forcing subset of W if W is the unique strong resolving set containing S. The forcing number f(W, sdim(G)) of W in G is the minimum cardinality of a forcing subset for W, while the forcing strong metric dimension, fsdim(G), of G is the smallest forcing number among all strong resolving sets of G. The forcing strong metric dimensions of some well-known graphs are determined. It is shown that for any positive integers a and b, with 0 ≤ a ≤ b, there is nontrivial connected graph G with sdim(G) = b and fsdim(G) = a if and only if {a, b} = {0, 1}.

UR - http://www.scopus.com/inward/record.url?scp=85036593284&partnerID=8YFLogxK

M3 - Artículo

AN - SCOPUS:85036593284

SN - 1715-0868

VL - 12

SP - 1

EP - 10

JO - Contributions to Discrete Mathematics

JF - Contributions to Discrete Mathematics

IS - 2

ER -