Structure and pancyclicity of maximal planar graphs with diameter two

Shu-Yu Cui, Yiqiao Wang, Danjun Huang, Hongwei Du and Weifan Wang ()
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Shu-Yu Cui: Zhejiang Normal University
Yiqiao Wang: Beijing University of Chinese Medicine
Danjun Huang: Zhejiang Normal University
Hongwei Du: Harbin Institute of Technology
Weifan Wang: Zhejiang Normal University

Journal of Combinatorial Optimization, 2022, vol. 43, issue 1, No 1, 27 pages

Abstract: Abstract A graph G on n vertices is called non-universal if its maximum degree is at most $$n-2$$ n - 2 . In this paper, we give a structural characterization for non-universal maximal planar graphs with diameter two. In precise, we find 10 basic graphs, and then generate all 25 non-universal maximal planar graphs with diameter two by adding repeatedly and appropriately 3-vertices to some of these 10 basic graphs. As an application, we show that maximal planar graphs with diameter two are pancyclic except five special graphs.

Keywords: Maximal plane graph; Diameter two; Pancyclicity; Dominating set (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00749-7

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