Graceful labeling of dihedral cayley graphs

Author: xocw

August undefined, 2024

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.

1 Introductory remarks

http://fs.unm.edu/IJMC/AStudyOnCayleyGraphsOverDihedralGroups.pdf 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 … inclusion\\u0027s s8

A Study on Cayley Graphs over Dihedral Groups - University …

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. WebFeb 15, 2024 · In this paper, we construct some directed strongly regular Cayley graphs on Dihedral groups, which generalizes some earlier constructions. We also characterize … WebIn this paper one of such labeling technique, namely Edge vertex prime labeling is applied on the well known algebraic structured Cayley graphs. It was introduced by Arthur Cayley in 1878 to illustrate the concept of abstract groups. Related Papers Arxiv preprint arXiv:1012.0537 Rough ends of infinite primitive groups 2010 • Simon Smith inclusion\\u0027s sg

Distance-regular Cayley graphs on dihedral groups - CORE

Non-normal one-regular and 4-valent Cayley graphs of …

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, where s∈ Sand t∈ T. Particularly, let T= {1G}. Then such a Smarandache-Cayley graph is the usual Cayley graph Cay(G,S), whose vertex set is Gand WebOct 24, 2024 · The finite dihedral group generated by one rotation and one flip is the simplest case of the non-Abelian group. Cayley graphs are diagrammatic counterparts … inclusion\\u0027s sbWebDec 23, 2024 · The Cayley graphs of crystallographic groups G_ {p}^ {p}, constructed on the minimal number of generators, are discussed. Some theorems on the existence of … inclusion\\u0027s sc

"WebDih 4 Cayley Graph; generators a, b; prefix.svg. The same file with right action (which is more usual for Cayley graphs). One of the Cayley graphs of the dihedral group Dih 4. … " - Graceful labeling of dihedral cayley graphs

Graceful labeling of dihedral cayley graphs

Graceful Labeling -- from Wolfram MathWorld

WebCayley Graphs Abstract There are frequent occasions for which graphs with a lot of sym-metry are required. One such family of graphs is constructed using ... Example 0.8 The dihedral group D 4 is the group of rigid-body motions on the unit square. Let rdenote a 90 clockwise rotation and let sdenote a re ection through a vertical axis. Then the http://www1.cs.columbia.edu/~cs6204/files/Lec6-CayleyGraphs.pdf

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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). Web3.2: Visualizing Groups- Cayley Graphs. So far, we've seen three different kinds of groups: Groups of symmetries (including the dihedral group of symmetries of a polygon), the …

Webgroups. We show that for any m E {I, 2, 3}, the dihedral group D2k is m-DCI if and only if D2k is m-CI if and only if 2 f k. § 1. Preliminaries Let G be a finite group and 5 a subset of G with 1 1:. 5. We use r = Cay( G; 5) to denote the Cayley digraph of G with respect to 5, defined to be the directed graph WebJun 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 …

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 ... Web35 rows · Mar 24, 2024 · A graceful labeling (or graceful numbering) is …

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 …

WebCayley 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 inclusion\\u0027s sdWebAug 1, 2005 · AbstractA Cayley map is a Cayley graph embedded in an orientable surface such that the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, … inclusion\\u0027s slWebCayley graphs of dihedral groups [10]. This work motivated us to study non-normal one-regular tetravalent Cayley graphs of dihedral groups. In this paper, we shall classify non-normalone-regularCayley graphsofD2n of valency 4. Now we state the main result of this paper. Theorem 1. Let X = Cay(G,S) be a one-regular and4-valent Cayley graph for ... inclusion\\u0027s sjWebCayley 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 ... inclusion\\u0027s shWebMay 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- … inclusion\\u0027s smWebCayley 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. inclusion\\u0027s sohttp://fs.unm.edu/IJMC/AStudyOnCayleyGraphsOverDihedralGroups.pdf inclusion\\u0027s sk