Minimum Neighborhood of Alternating Group Graphs
The minimum neighborhood and combinatorial property are two important indicators of fault tolerance of a multiprocessor system. Given a graph G , θ G (q) is the minimum number of vertices adjacent to a set of q vertices of G (1 ≤|V(G)| ). It is meant to determine θ G (q), the minimum neighborhood problem (MNP). In this paper, we obtain θ AGn (q) for an independent set with size q in an n -dimensional alternating group graph AG n , a well-known interconnection network for multiprocessor systems. We first propose some combinatorial properties of AG n . Then, we study the MNP for an independent set of two vertices and obtain that θ AGn (2)=4n-10. Next, we prove that θ AGn (3)=6n-16. Finally, we propose that θ AGn (4)=8n-24.
MSU Digital Commons Citation
Huang, Yanze; Lin, Limei; Wang, Dajin; and Xu, Li, "Minimum Neighborhood of Alternating Group Graphs" (2019). Department of Computer Science Faculty Scholarship and Creative Works. 403.