Graceful labeling of dihedral cayley graphs
WebJan 1, 2024 · prime labeling of Cayley graph depending upon the generating ... dihedral group of order 16 and let ... A function f is called a graceful labeling of a graph G with q … WebNov 1, 2024 · A cubic graph Γ is called G-symmetric if a group G of automorphisms of Γ acts transitively on the arcs of Γ, and G-basic if it is G-symmetric and G has no non-trivial normal subgroups with more than two orbits on the vertex set of Γ. We say the graph Γ is basic if it is G-basic for all arc-transitive subgroups G of Aut (Γ).All basic symmetric cubic …
Graceful labeling of dihedral cayley graphs
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Web35 rows · Mar 24, 2024 · A graceful labeling (or graceful numbering) is … WebMay 27, 2024 · A Cayley (di)graph of a group with respect to is said to be normal if the right regular representation of is normal in the automorphism group of , and is called a CI- (di)graph if there is such that , whenever for a Cayley (di)graph . A finite group is called a DCI-group or a NDCI-group if all Cayley digraphs or normal Cayley digraphs of are CI ...
Web1. Cayley Graphs We begin by giving a very brief introduction to the topic of graphs with an emphasis on Cayley graphs, which will be the focus of all of our examples in section 3. We assume some familiarity with groups. De nition 1.1. A graph is a pair = ( V;E);where V is a set of points called vertices and Eis a collection of vertex pairs ... WebIn this paper, we study perfect state transfer on Cayley graphs over dihedral groups. Using the representations of the dihedral group , we present some necessary and sufficient …
WebFeb 25, 2024 · Axioms 2024, 11, 100 2 of 14 Theorem 1. The graph BGn is a Cayley graph on some group G = hf, Aiof dihedral type with f: (p) $[p] 2Aut(BGn) and A uniform if and only if the function system Fn = ffi ji = 2,. . .,ngis Cayley graphic of dihedral type (see Definition 5) in R. Cayley graphs are widely studied together with Hamiltonian graphs … WebA Smarandache-Cayley graph of Grespect to a pair {S,T} of non-empty subsets S⊂ G, T⊂ G\Sis the graph with vertex set Gand edge set consisting of pairs (x,y) such that s·x= t·y, …
WebA graph G is called bi-edge - graceful if both G and its line graph L(G) are edge - graceful. Therefore the Complement of Cayley digraph C. Cay (G,S) with S ≡ 0(mod2) is bi - edge – graceful. Corollary Every cayley digraph admits edge graceful labeling only when S ≡ 1(mod2) but its complement is edge graceful only when S ≡ 0(mod2).
WebThe Cayley graph X(G,S) is called a CI-graphof G if, for any Cayley graph X(G,T), whenever X(G,S) ˙ X(G,T) we have σ(S) = T for some σ∈ Aut(G). A group G is called a CI-groupif all Cayley graphs on G are CI-graphs. A long-standing open question about Cayley graphs is as follows: which Cayley graphs for a group G are CI-graphs? northampton district nursesWebMar 24, 2024 · An undirected Cayley graph of a particular generating set of the alternating group is sometimes known as a alternating group graph . The Cayley graph of the cyclic group is the cycle graph , and of the … northampton diocese websiteWebFeb 15, 2024 · In this paper, we construct some directed strongly regular Cayley graphs on Dihedral groups, which generalizes some earlier constructions. We also characterize … northampton district court maWebJan 1, 2013 · A Cayley digraph is a digraph constructed from a group Γ and a generating subset S of Γ. It is denoted by Cay D (Γ,S). In this paper, we prove for any finite group Γ … northampton district attorney\u0027s officeWebCayley graph on the non-abelian non-dihedral group of order 12. The Heawood graph and its bipartite complement are distance-regular Cayley graphs on the dihedral group of order 14, and as it was pointed out in [10], the Shrikhande graph can be represented as a Cayley graph on three non-isomorphic non-abelian groups of order 16, as well as a ... northampton diocese facebookWebCayley graphs over non-Abelian groups. Key Words: Cayley graphs, Hamiltonian cycles and paths, complete graph, orbit and centralizer of an element in a group, centre of a group. AMS(2010): 05C25 §1. Introduction Let Gbe a finite group and Sbe a non-empty subset of G. The graph Cay(G,S) is defined northampton dinerhttp://fs.unm.edu/IJMC/AStudyOnCayleyGraphsOverDihedralGroups.pdf how to repair rear demister