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Alternative Domination in Graphs
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PRE
AI
DOI：10.1080/09728600.2025.2559653.png)
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Abstract
En 中文
Sometimes while you are using the Internet, for example, via a Wi-Fi network from one of the companies, the Internet is suddenly cut off due to a malfunction at that point, which disrupts your important work on the Internet, so there is a need for another source close to this point through which you can operate the Internet until this malfunction is fixed. To contribute to solving this problem, we assume that the two Wi-Fi points are D1 and D2, and the person using it is v such that v is adjacent to a vertex x is an element of D1 and a vertex y is an element of D2. In this paper, we introduce the concept of an alternative domination that models the aforementioned problem. Specifically, a dominating set D=D1 boolean OR D2 of a graph G=(V,E) is said to be an alternative domination if every vertex v is an element of V-D has at least one neighbor in D1 and one neighbor in D2. The cardinality of a minimum alternative dominating set in G is called the alternative domination number of G and is denoted by gamma 1,2(G). Basic properties and some interesting results have been obtained.
Keywords:
Alternative domination number
domination number
connected domination number
Journal
A
IF:
0.7
Papers:
20
Citations:
0
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