Partial profiles of quasi-complete graphs
Pedro Lopes
TL;DR
This paper counts graph homomorphisms from various source graphs to quasi-complete graphs, revealing new two-parameter integer sequences related to graph structure and mappings.
Contribution
It provides the first enumeration of homomorphisms to quasi-complete graphs from multiple source graph classes, introducing new two-dimensional integer sequences.
Findings
Enumerations for complete, quasi-complete, cycle, path, wheel, and broken wheel source graphs.
Development of two-parameter sequences indexed by source and target graph sizes.
Insights into the structure of graph homomorphisms to quasi-complete graphs.
Abstract
We enumerate graph homomorphisms to quasi-complete graphs, i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasi-complete graphs, cycles, paths, wheels and broken wheels. These enumerations give rise to sequences of integers with two indices; one of the indices is the number of vertices of the source graph, and the other index is the number of vertices of the target graph.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Limits and Structures in Graph Theory