Summary: 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.

05A15, 05C15

enumeration, sequence of integers, graph, graph homomorphism, complete graph, quasi-complete graph, path, cycle, wheel, broken wheel, lovász vector of graph (profile of graph)