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1.
Extremal edge general position sets in some graphs
Jing Tian, Sandi Klavžar, Elif Tan, 2024, original scientific article

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 graphs
Published in DiRROS: 27.03.2024; Views: 108; Downloads: 47
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2.
The cut method on hypergraphs for the Wiener index
Sandi Klavžar, Gašper Domen Romih, 2023, original scientific article

Abstract: The cut method has been proved to be extremely useful in chemical graph theory. In this paper the cut method is extended to hypergraphs. More precisely, the method is developed for the Wiener index of $k$-uniform partial cube-hypergraphs. The method is applied to cube-hypergraphs and hypertrees. Extensions of the method to hypergraphs arising in chemistry which are not necessary $k$-uniform and/or not necessary linear are also developed.
Keywords: hypergraphs, Wiener index, cut method, partial cube-hypergraphs, hypertrees, phenylene, Clar structures
Published in DiRROS: 15.03.2024; Views: 102; Downloads: 49
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