THE (𝟏, 𝟐)-INTERSECTION INDEX OF A GRAPH WITH LARGE MINIMUM DEGREE AND ITS APPLICATION IN CRISIS MANAGEMENT
Paweł Bednarz, Adrian Michalski · Scientific Papers of Silesian University of Technology Organization and Management Series · 2024
Purpose: The purpose of this paper is to prove the conjecture which states that the (1, 2 ̅ )-intersection index of a graph with δ(𝐺) ≥ 3 is equal to zero.Moreover, practical applications of this result are given.Design/methodology/approach: We prove the conjecture by considering cases and indicating in each case two disjoint sets such that one of them is a (1, 1)-dominating set and the second one is a proper (1, 2)-dominating set.We also use a graph to model the problem of storage of supplies in Poland in case of a crisis.Findings: For every connected graph, in which every vertex has at least three neighbors, the (1, 2 ̅ )-intersection index is equal to zero.It ensures that in most cases there exists an optimal allocation of water and food supplies throughout a given region.Practical implications: The findings may be used by crisis management services when planning the allocation of food and water reserves.Originality/value: The obtained results and applications are new and original, they may be of value to mathematician working in the field of theoretical and applied graph theory, as well as to researchers working on crisis management and methods of efficient supply allocations.