Abstract: 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.Keywords: general position set, edge general position set, cut-vertex, diametral path, block graphsPublished in DiRROS: 27.03.2024; Views: 285; Downloads: 140 Full text (304,95 KB)This document has many files! More...
Abstract: 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 in $G$. The cardinality of a largest edge general position set of $G$ is the edge general position number of $G$. In this paper edge general position sets are investigated in partial cubes. In particular it is proved that the union of two largest $\Theta$-classes of a Fibonacci cube or a Lucas cube is a maximal edge general position set.Keywords: general position set, edge general position sets, partial cubes, Fibonacci cubes, Lucas cubesPublished in DiRROS: 18.03.2024; Views: 298; Downloads: 129 Full text (424,01 KB)This document has many files! More...
