TY - JOUR
TI - On 2-Resolving Dominating Sets in the Join, Corona and Lexicographic Product of Two Graphs
PY - 2022/07/31
Y2 - 2024/04/24
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 15
IS - 3
DO - 10.29020/nybg.ejpam.v15i3.4426
UR - https://doi.org/10.29020/nybg.ejpam.v15i3.4426
SP - 1417-1425
AB - Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set for G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions. A 2-resolving set S ⊆ V (G) which isdominating is called a 2-resolving dominating set or simply 2R-dominating set in G. The minimum cardinality of a 2-resolving dominating set in G, denoted by γ2R(G), is called the 2R-domination number of G. Any 2R-dominating set of cardinality γ2R(G) is then referred to as a γ2R-set in G. This study deals with the concept of 2-resolving dominating set of a graph. It characterizes the 2-resolving dominating set in the join, corona and lexicographic product of two graphs and determine the bounds or exact values of the 2-resolving dominating number of these graphs.
ER -