On the transmission of uniform unicyclic hypergraphs
Hongying Lin, Bo Zhou
TL;DR
This paper investigates the transmission metric in uniform unicyclic hypergraphs, identifying those with the smallest and largest total distances among vertices for a given size.
Contribution
It uniquely characterizes the unicyclic hypergraphs with extremal transmission values among all fixed-size uniform unicyclic hypergraphs.
Findings
Identifies the hypergraph with minimum transmission.
Identifies the hypergraph with maximum transmission.
Provides a complete characterization of extremal cases.
Abstract
The transmission of a connected hypergraph is defined as the summation of distances between all unordered pairs of distinct vertices. We determine the unique uniform unicyclic hypergraphs of fixed size with minimum and maximum transmissions, respectively.
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Taxonomy
TopicsGraph theory and applications · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems