On the number of congruence classes of paths
Copyright policy )On the number of congruence classes of paths
Let $P_n$ denote the undirected path of length $n-1$. The cardinality of the set of congruence classes induced by the graph homomorphisms from $P_n$ onto $P_k$ is determined. This settles an open problem of Michels and Knauer (Disc. Math., 309\ (2009)\ 5352-5359). Our result is based on a new proven formula of the number of homomorphisms between paths.
11 pages, 2 figures, to appear in Discrete Mathematics
- University of Lyon System France
- Lanzhou University China (People's Republic of)
- Claude Bernard University Lyon 1 France
- UNIVERSITE JEAN MONNET SAINT-ETIENNE France
- Jean Monnet University France
paths, Graph endomorphisms, Graph homomorphisms, Paths, graph homomorphisms, graph, Enumeration in graph theory, Graph, 004, 510, Theoretical Computer Science, lattice paths, Lattice paths, graph endomorphisms, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Paths and cycles
paths, Graph endomorphisms, Graph homomorphisms, Paths, graph homomorphisms, graph, Enumeration in graph theory, Graph, 004, 510, Theoretical Computer Science, lattice paths, Lattice paths, graph endomorphisms, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Paths and cycles
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