On the structure of pentagraphs

Yian Xu

Applied Mathematics and Computation, 2023, vol. 439, issue C

Abstract: A pentagraph is a simple graph without cycles on 3 or 4 vertices and without induced cycles of odd length at least 7. In this paper, we present some structural properties of pentagraphs. As a corollary, we give a short proof that there is exactly one 3-connected internally 4-connected non-bipartite cubic pentagraph, which is the Petersen graph.

Keywords: Triangle; Odd hole; Petersen graph (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322007044

DOI: 10.1016/j.amc.2022.127632

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