Neighbor Connectivity of the Alternating Group Graph
Given a graph G=(V,E), its neighbor connectivity is the least number of vertices whose deletion along with their neighbors results in a disconnected, complete, or empty graph. The edge neighbor connectivity is the least number of edges whose deletion along with their endpoints results in a disconnec...
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| Published: |
2021
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| Online Access: | https://dspace.auk.edu.kw/handle/11675/8179 https://doi.org/10.1142/S0219265921500146 |
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| Summary: | Given a graph G=(V,E), its neighbor connectivity is the least number of vertices whose deletion along with their neighbors results in a disconnected, complete, or empty graph. The edge neighbor connectivity is the least number of edges whose deletion along with their endpoints results in a disconnected, complete, or empty graph. In this paper, we determine the neighbor connectivity κNB and the edge neighbor connectivity λNB of the alternating group graph. We show that κNB(AGn)=λNB(AGn)=n−2, where AGn is the n-dimensional alternating group graph. |
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