On some metric properties of direct-co-direct product

Aleksander Kelenc and Iztok Peterin

Applied Mathematics and Computation, 2023, vol. 457, issue C

Abstract: Direct-co-direct product G⊛H of graphs G and H is a graph on vertex set V(G)×V(H). Two vertices (g,h) and (g′,h′) are adjacent if gg′∈E(G) and hh′∈E(H) or gg′∉E(G) and hh′∉E(H). We show that eccentricity of a vertex of G⊛H for connected non-complete graphs G and H is bounded by five. In addition, we fully describe when the eccentricity is four or five and in all cases one factor must be a star. This is a cornerstone for the distance formula for G⊛H. The disconnected cases of G⊛H are also characterized along the way.

Keywords: Direct-co-direct product; Distance; Eccentricity; Connected graph (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003211

DOI: 10.1016/j.amc.2023.128152

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