Irreversible k-threshold conversion number of some graphs
| Autor: | Ramy Shaheen, Suhail Mahfud, Ali Kassem |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Arab Journal of Mathematical Sciences, Vol 30, Iss 1, Pp 43-56 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2588-9214 1319-5166 |
| DOI: | 10.1108/AJMS-07-2021-0150/full/pdf |
| Popis: | Purpose – This paper aims to study Irreversible conversion processes, which examine the spread of a one way change of state (from state 0 to state 1) through a specified society (the spread of disease through populations, the spread of opinion through social networks, etc.) where the conversion rule is determined at the beginning of the study. These processes can be modeled into graph theoretical models where the vertex set V(G) represents the set of individuals on which the conversion is spreading. Design/methodology/approach – The irreversible k-threshold conversion process on a graph G=(V,E) is an iterative process which starts by choosing a set S_0?V, and for each step t (t = 1, 2,…,), S_t is obtained from S_(t−1) by adjoining all vertices that have at least k neighbors in S_(t−1). S_0 is called the seed set of the k-threshold conversion process and is called an irreversible k-threshold conversion set (IkCS) of G if S_t = V(G) for some t = 0. The minimum cardinality of all the IkCSs of G is referred to as the irreversible k-threshold conversion number of G and is denoted by C_k (G). Findings – In this paper the authors determine C_k (G) for generalized Jahangir graph J_(s,m) for 1 |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|