The Modular Group and Cayley Graphs
On the automorphism group of Cayley graphs generated by transpositions
... the Cayley graph of S n generated by n cyclically adjacent ...automorphism group of the modified bubble sort graph of dimension n is S n × D 2n , for all n ≥ ...automorphism group of the modified ...
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On covers of graphs by Cayley graphs
... infinite group weakly residually finite, if all its Cayley graphs G have the following property: for every r ∈ N , there is a finite graph H which is ...finite group is weakly residually ...
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Bounds for Domination Parameters in Cayley Graphs on Dihedral Group
... the Cayley graph G = Cay(D 2n , Ω) constructed on the finite dihedral group D 2n , and a specified generating set Ω of D 2n ...of Cayley graphs on the dihe- dral group is also ...
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Connectedness of spheres in Cayley graphs
... Connectedness of spheres in Cayley graphs Jérémie Brieussel and Antoine Gournay ∗ Communicated by R. I. Grigorchuk A b s t r ac t . We introduce the notion of connection thickness of spheres in a ...
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Cayley Graphs of Groups and Their Applications
... EXAMPLE 4.17: Find a hamiltonian cycle on Z 7 o 2 Z 3 . Consider the following image. Figure 21: A hamiltonian cycle in Z 7 o 2 Z 3 . In Fig. 21, reorganize the vertices of Z 7 o 2 Z 3 in the above manner. The first row ...
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Some Properties of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs
... product graphs). Let and be two simple graphs with their vertex sets as { } and { } ...two graphs denoted by is defined to be a graph with vertex set , where is the Cartesian product of the sets and ...
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On the normality of Cayley graphs of order pq ∗
... The Cayley digraph Γ = Cay(G, S) is called normal for group G if R(G) ...of Cayley digraphs, which is known to be very difficult in ...all Cayley digraphs into two classes: normal and ...
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3 Quasi 2-Cayley graphs
... Proof of the Theorem 1.2: Let Γ be a connected circulant of order n, which is also a quasi 3-Cayley on a group G. The point at infinity is adjacent to all three nontrivial orbits of G, if and only if Γ is ...
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Unitary Addition Cayley Signed Graphs
... addition Cayley sigraph Σ n , if n = p a , then U n consists of all the numbers less than n, which are not multiples of ...addition Cayley sigraph, we have a negative edge only when αp is adjacent to β ...
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Isomorphisms of Cayley graphs of surface groups
... the Cayley graph of the fundamental group Γ g of the closed, ori- entable surface of genus g ≥ 2 with respect to the usual generating set is isomorphic to the Cayley graph of a certain Coxeter ...
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Labelled Cayley graphs and minimal automata
... Abstract Cayley graphs considered as language recognisers are as powerful as the more general finite state ...applies Cayley graphs to define a class of automata and describe minimal automata of ...
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Large butterfly Cayley graphs and digraphs
... directed Cayley graphs whose construction is related to butterfly ...known Cayley graphs and digraphs of diameter k and degree ...d, Cayley graphs and digraphs of diameter k and ...
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On Planar Cayley graphs and Kleinian groups
... a Cayley graph of Γ, but the freeness condition is not necessarily satisfied because some involution g ∈ Γ might exchange two crossing arcs R s , gR s , hence stabilising their intersection ...
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Diameters of Cayley graphs of Chevalley groups
... Chevalley group over Z/kZ we could define the notion of ‘row’ and ‘column’ matrices and modify then generalize the proof of Theorem ...Chevalley group over ...
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Iterative Construction of Cayley Expander Graphs
... Schreier graphs, free from the seed graph on the alternating ...symmetry group of the infinite rooted d-regular ...expander Cayley graph on the (alternating) group of symmetries of this finite ...
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The Directed Forest Complex of Cayley Graphs
... 2. Suppose that T a directed tree in Γ that is not contained in a bigger directed tree. We will show that T contains all vertices of Γ. Let r be the root of T . Suppose that v is a vertex not contained in T . Note that ...
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Vector Space semi-Cayley Graphs
... the group is excluded S. In this case, the uncolored Cayley graph is a simple undirected ...A Cayley graph is connected if and only if G = hSi. In general the Cayley graph over the ...
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A note on orbit graphs of finite groups and colour-clique graphs of Cayley graphs
... [1], the possibility u = v was allowed in the description of adjacency by intersection, thus giving rise to loops at every vertex. A number of properties of G-graphs were further studied in [2, 4, 5, 6, 7]. The ...
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Matching Dominating Sets of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs
... Product Graphs Products of graphs occur naturally in discrete mathematics as tools in combinatorial ...of graphs and deep structural ...of graphs, which are referred as product ...
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Some Domination Parameters of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs
... of graphs, namely Arithmetic Graphs by introducing the concepts of Number Theory, particularly, the Theory of Congruences in Graph ...Theory. Cayley graphs are another class of graphs ...
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