2025/03/02 by Midhuna V Ajith, Ajith, Midhuna V, Mainak Ghosh +3
Computer Science · #05C20 #05C25 #08A35 #Advanced Graph Theory Research #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2503.00759
openalex publication_date 2025/03/02 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
Let G be a group. The directed endomorphism graph, \dend of G is a directed graph with vertex set G and there is a directed edge from the vertex `a' to the vertex ` b' (a ≠ b) if and only if there exists an endomorphism on G mapping a to b. The endomorphism graph, \uend of G is the corresponding undirected simple graph. The automorphism graph, Auto(G) of G is an undirected graph with vertex set G and there is an edge from the vertex `a' to the vertex ` b' (a ≠ b) if and only if there exists an automorphism on G mapping a to b. We have explored graph theoretic properties like size, planarity, girth etc. and tried finding out for which types of groups these graphs are complete, diconnected, trees, bipartite and so on.