arXiv:2409.00268 Abstract | arXiv Analytics

arXiv:2409.00268 [math.CO]Abstract References Reviews Resources

Uniform Shared Neighborhood Structures in Edge-Regular Graphs

Published 2024-08-30Version 1

A shared neighborhood structure (SNS) in a graph is a subgraph induced by the intersection of the open neighbor sets of two adjacent vertices. If a SNS is the same for all adjacent vertices in an edge-regular graph, call the SNS a uniform shared neighborhood structure (USNS). USNS-forbidden graphs (graphs which cannot be a USNS of an edge-regular graph) and USNS in graph products of edge-regular graphs are examined.

Comments: 15 pages, 4 figures

Categories: math.CO

Subjects: 05C75, 05C76

Keywords: uniform shared neighborhood structure, edge-regular graph, adjacent vertices, open neighbor sets, usns-forbidden graphs

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