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Povzetek: A set of edges $X\subseteq E(G)$ of a graph $G$ is an edge general position set if no three edges from $X$ lie on a common shortest path. The edge general position number ${\rm gp}_{\rm e}(G)$ of $G$ is the cardinality of a largest edge general position set in $G$. Graphs $G$ with ${\rm gp}_{\rm e}(G) = |E(G)| - 1$ and with ${\rm gp}_{\rm e}(G) = 3$ are respectively characterized. Sharp upper and lower bounds on ${\rm gp}_{\rm e}(G)$ are proved for block graphs $G$ and exact values are determined for several specific block graphs.
Ključne besede: general position set, edge general position set, cut-vertex, diametral path, block graphs
Objavljeno v DiRROS: 27.03.2024; Ogledov: 108; Prenosov: 47
Celotno besedilo (304,95 KB)
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