Locating-dominating coalitions in graphs
M. Chellali, A. A. Dobrynin, F. Foucaud, H. Golmohammadi, J.C. Valenzuela-Tripodoro

TL;DR
This paper introduces the concept of locating-dominating coalitions in graphs, explores their existence, bounds, and exact values for certain graph classes, and studies the computational complexity of related decision problems.
Contribution
It initiates the study of locating-dominating coalitions, providing bounds, characterizations, exact values for specific graphs, and analyzing the complexity of associated decision problems.
Findings
Characterized graphs with maximum coalition number
Established bounds on the coalition number
Determined exact coalition numbers for certain graph classes
Abstract
A set of vertices in a graph is a locating-dominating set (LD-set) if it is dominating and every two vertices , of satisfy . Two disjoint sets form a locating-dominating coalition (for short, an LD-coalition) in if none of them is an LD-set in but their union is an LD-set. A locating-dominating coalition partition (for short, an LDC-partition) is a vertex partition such that every set of is not an LD-set in but forms an LD-coalition with another set of . The locating-domination coalition number of , denoted by equals the maximum cardinality of an LDC-partition of . Our purpose in this paper is to initiate the study of locating-dominating coalitions in graphs. We first investigate the existence of LDC-partitions. We also obtain lower and upper…
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Taxonomy
TopicsGame Theory and Voting Systems · Advanced Graph Theory Research · Complexity and Algorithms in Graphs
