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Distance formula for direct-co-direct product in the case of disconnected factorsAleksander Kelenc,
Iztok Peterin, 2023, izvirni znanstveni članek
Povzetek: Direct-co-direct product $G\circledast H$ of graphs $G$ and $H$ is a graph on the vertex set $V(G)\times V(H)$. Two vertices $(g,h)$ and $(g',h')$ are adjacent if $gg'\in E(G)$ and $hh'\in E(H)$ or $gg'\notin E(G)$ and $hh'\notin E(H)$. We show that if at most one factor of $G\circledast H$ is connected, then the distance between two vertices of $G\circledast H$ is bounded by three unless some small number of exceptions. All the exceptions are completely described which yields the distance formula.
Ključne besede: direct-co-direct product, distance, eccentricity, disconnected graphs
Objavljeno v DiRROS: 19.03.2024; Ogledov: 80; Prenosov: 45
Celotno besedilo (450,88 KB)
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