Graceful labeling of dihedral cayley graphs
WebHere's the construction of a Cayley graph for a group G with generators {a 1, a 2 ,...,a m } in 3 easy steps: Draw one vertex for every group element, generator or not. (And don't forget the identity!) For every generator a j, connect vertex g to ga j by a directed edge from g to ga j. Label this edge with the generator. WebA method for relaxed graceful labeling of P2n graphs is presented together with an algorithm designed for labeling these graphs. Graceful labeling is achieved by relaxing the range to 2m and ...
Graceful labeling of dihedral cayley graphs
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In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and m inclusive. A graph which admits a graceful labeling is called a graceful graph. 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 ...
WebJul 10, 2024 · In this research work, we prove that the ladder graph admits the-graceful labeling. The ladder graph is a graph obtained from the Cartesian product of and 2. Moreover, we studied the-grace-fulness ... WebCayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the dihedral group. Considering the characteristics of the elements in the dihedral group, we conduct the model of discrete-time quantum walk on the Cayley graph of the dihedral group by special coding mode.
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). WebJan 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 …
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WebMay 27, 2024 · Graceful Labeling of Graphs. Cindy Aossey and Dee Crescitelli started the session with a notice and wonder about two graphs. Our group’s noticings included: In … black and blue granite countertopsWebJan 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 … black and blue guitar tabWebFeb 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 … davao city risk reductionWebNov 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 … black and blue gradient nailsWebFeb 15, 2024 · In this paper, we construct some directed strongly regular Cayley graphs on Dihedral groups, which generalizes some earlier constructions. We also characterize … black and blue graphic hoodiesWebApr 9, 2015 · If our Cayley graph edges are defined (as in the Wolfram article) by left multiplication, then right multiplication will give graph isomorphisms. However, if our Cayley graph edges are defined (as by Derek) by right multiplication, then left multiplication will give graph isomorphisms. black and blue guinness and blue moonWebJun 15, 2024 · In this paper, we reveal the relations between perfect state transfer and perfect edge state transfer on Cayley graphs. Furthermore, we present necessary and … davao city products