نتایج جستجو برای: bi cayley graph
تعداد نتایج: 244893 فیلتر نتایج به سال:
Nathanson was the pioneer in introducing the concepts of Number Theory, particularly, the "Theory of Congruences" in Graph Theory, thus paving way for the emergence of a new class of graphs, namely "Arithmetic Graphs". Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley g...
The question of which groups admit planar Cayley graphs goes back over 100 years, being settled for finite groups by Maschke in 1896. Since that time, various authors have studied infinite planar Cayley graphs which satisfy additional special conditions. We consider the question of which groups possess any planar Cayley graphs at all by categorizing such graphs according to their connectivity. ...
The Cayley Isomorphism property for combinatorial objects was introduced by L. Babai in 1977. Since then it has been intensively studied for binary relational structures: graphs, digraphs, colored graphs etc. In this paper we study this property for oriented Cayley maps. A Cayley map is a Cayley graph provided by a cyclic rotation of its connection set. If the underlying graph is connected, the...
For any finite abelian group G and any subset S ⊆ G, we determine the connectivity of the addition Cayley graph induced by S on G. Moreover, we show that if this graph is not complete, then it possesses a minimum vertex cut of a special, explicitly described form. 1. Background: addition Cayley graphs For a subset S of the abelian group G, we denote by Cay+G(S) the addition Cayley graph induced...
Let be a connected Cayley graph of group G, then Γ is called normal if the right regular representation of G is a normal subgroup of , the full automorphism group of Γ. For the case where G is a finite nonabelian simple group and Γ is symmetric cubic Cayley graph, Caiheng Li and Shangjin Xu proved that Γ is normal with only two exceptions. Since then, the normality of nonsymmetric cubic Cayley ...
Static DHT topologies influence important features of such DHTs such as scalability, communication load balancing, routing efficiency and fault tolerance. Nevertheless, it is commonly recognized that the primary difficulty in designing DHT is not in static DHT topologies, but in the dynamic DHT algorithm which adapts various static DHT topologies to a dynamic network at Internet. As a direct co...
A Cayley graph Cay(G,S) on a group G with respect to a Cayley subset S is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay(G,S). For a positive integer n, let Γn be a graph having vertex set {xi, yi | i ∈ Z2n} and edge set {{xi, xi+1}, {yi, yi+1}, {x2i, y2i+1}, {y2i, x2i+1} | i ∈ Z2n}. In this paper, it is shown that Γn is a Cayley ...
Cayley polytopes were defined recently as convex hulls of Cayley compositions introduced by Cayley in 1857. In this paper we resolve Braun’s conjecture, which expresses the volume of Cayley polytopes in terms of the number of connected graphs. We extend this result to two one-variable deformations of Cayley polytopes (which we call t-Cayley and t-Gayley polytopes), and to the most general two-v...
For a positive integer s, a graph Γ is called s-arc transitive if its full automorphism group AutΓ acts transitively on the set of s-arcs of Γ . Given a group G and a subset S of G with S = S−1 and 1 / ∈ S, let Γ = Cay(G, S) be the Cayley graph of G with respect to S and G R the set of right translations of G on G. Then G R forms a regular subgroup of AutΓ . A Cayley graph Γ = Cay(G, S) is call...
Let G be a finite group, S ⊆ G \ {1} be a set such that if a ∈ S, then a−1 ∈ S, where 1 denotes the identity element of G. The undirected Cayley graph Cay(G, S) ofG over the set S is the graphwhose vertex set is G and two vertices a and b are adjacent whenever ab−1 ∈ S. The adjacency spectrum of a graph is the multiset of all eigenvalues of the adjacency matrix of the graph. A graph is called i...
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