RT journal article
T1 The forcing total restrained geodetic number and the total restrained geodetic number of a graph: Realizability and complexity
A1 Najimi, M.
A1 Abdollahzadeh Ahangar, H.
A1 Samodivkin, V.
A1 González Yero, Ismael
A2 Matemáticas
K1 Geodetic
K1 Total geodetic
K1 Total restrained geodetic number
K1 Forcing total restrained geodetic number
AB Given two vertices u and v of a nontrivial connected graph G, the set I[u,v] consists all vertices lying on some u−v geodesic in G, including u and v. For S⊆V(G), the set I[S] is the union of all sets I[u,v] for u,v∈S. A set S⊆V(G) is a total restrained geodetic set of G if I[S]=V(G) and the subgraphs induced by S and V(G)−S have no isolated vertex. The minimum cardinality of a total restrained geodetic set of G is the total restrained geodetic number gtr(G) of G and a total restrained geodetic set of G whose cardinality equals gtr(G) is a minimum total restrained geodetic set of G. A subset T of a minimum total restrained geodetic set S is a forcing subset for S if S is the unique minimum total restrained geodetic set of G containing T. The forcing total restrained geodetic number ftr(S) of S is the minimum cardinality of a forcing subset of S and the forcing total restrained geodetic number ftr(G) of G is the minimum forcing total restrained geodetic number among all minimum total restrained geodetic sets of G. In this article we determine all pairs a,b of integers such that ftr(G)=a and gtr(G)=b for some nontrivial connected graph G. Moreover, we show that the decision problem regarding that the total restrained geodetic number of a graph will be less than some positive integer r is NP-complete even when restricted to chordal graph.
PB Kalasalingam University
SN 0972-8600
YR 2017
FD 2017
LK http://hdl.handle.net/10498/33948
UL http://hdl.handle.net/10498/33948
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026