Semisymmetric \(Z_p\)-covers of the \(C20\) graph. (English) Zbl 1473.05128
Summary: A graph \(X\) is said to be \(G\)-semisymmetric if it is regular and there exists a subgroup \(G\) of \(A := \operatorname{Aut}(X)\) acting transitively on its edge set but not on its vertex set. In the case of \(G = A\), we call \(X\) a semisymmetric graph. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields. In this study, by applying concept linear algebra, we classify the connected semisymmetric \(z_p\)-covers of the \(C20\) graph.
MSC:
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
Keywords:
invariant subspaces; homology group; \(C20\) graph; semisymmetric graphs; regular covering; lifting automorphismsSoftware:
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