Geodesic
On walk domination: weakly toll domination, $l_2$ and $l_3$ domination
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 837-861

Voir la notice de l'article provenant de la source Library of Science

In this paper we study domination between different types of walks connecting two non-adjacent vertices of a graph. In particular, we center our attention on weakly toll walk and l_k-path for k ∈{2,3}. A walk between two non-adjacent vertices in a graph G is called a weakly toll walk if the first and the last vertices in the walk are adjacent, respectively, only to the second and second-to-last vertices, which may occur more than once in the walk. And an l_k-path is an induced path of length at most k between two non-adjacent vertices in a graph G. We study the domination between weakly toll walks, l_k-paths (k ∈{2,3}) and different types of walks connecting two non-adjacent vertices u and v of a graph (shortest paths, induced paths, paths, tolled walks, weakly toll walks, l_k-paths for k ∈{3,4}), and show how these give rise to characterizations of graph classes.
Keywords: domination, paths, geodesic, chordal graphs, interval graphs 
@article{DMGT_2024_44_3_a1,
     author = {Gutierrez, Marisa and Tondato, Silvia},
     title = {On walk domination: weakly toll domination, $l_2$ and $l_3$ domination},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {837--861},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a1/}
}
TY  - JOUR
AU  - Gutierrez, Marisa
AU  - Tondato, Silvia
TI  - On walk domination: weakly toll domination, $l_2$ and $l_3$ domination
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2024
SP  - 837
EP  - 861
VL  - 44
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a1/
LA  - en
ID  - DMGT_2024_44_3_a1
ER  - 
%0 Journal Article
%A Gutierrez, Marisa
%A Tondato, Silvia
%T On walk domination: weakly toll domination, $l_2$ and $l_3$ domination
%J Discussiones Mathematicae. Graph Theory
%D 2024
%P 837-861
%V 44
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a1/
%G en
%F DMGT_2024_44_3_a1
Gutierrez, Marisa; Tondato, Silvia. On walk domination: weakly toll domination, $l_2$ and $l_3$ domination. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 837-861. http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a1/