scholarly journals Super restricted edge-connectivity of vertex-transitive graphs

2004 ◽  
Vol 289 (1-3) ◽  
pp. 199-205 ◽  
Author(s):  
Ying Qian Wang
Keyword(s):  
Edge Connectivity ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

scholarly journals On the conditional edge connectivity of double-orbit graphs

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5935-5948
Author(s):  
Shuang Zhao ◽  
Jixiang Meng
Keyword(s):  
Fault Tolerance ◽  
Network Models ◽  
Sufficient Condition ◽  
Edge Connectivity ◽  
Important Index ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

The double-orbit graph is a generalization of vertex transitive graphs, which contains many classic network models. Conditional edge-connectivity is an important index to measure the fault-tolerance and reliability of the networks. In this paper, we characterize the super-?(2) double-orbit graphs with two orbits of the same size. Moreover, we give a sufficient condition for regular double-orbit graphs to be ?(3)-optimal, and characterize super- ?(3) regular double-orbit graphs.

On Super Restricted Edge Connectivity of Half Vertex Transitive Graphs

2011 ◽  
Vol 28 (2) ◽  
pp. 287-296
Author(s):  
Yingzhi Tian ◽  
Jixiang Meng ◽  
Xiaodong Liang
Keyword(s):  
Edge Connectivity ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

Trivalent Non-symmetric Vertex-Transitive Graphs of Order at Most 150

2008 ◽  
Vol 15 (03) ◽  
pp. 379-390 ◽  
Author(s):  
Xuesong Ma ◽  
Ruji Wang
Keyword(s):  
Automorphism Group ◽  
Bipartite Graphs ◽  
Type Ii ◽  
Symmetric Graph ◽  
Trivalent Graph ◽  
Block Graphs ◽  
Group A ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

Let X be a simple undirected connected trivalent graph. Then X is said to be a trivalent non-symmetric graph of type (II) if its automorphism group A = Aut (X) acts transitively on the vertices and the vertex-stabilizer Av of any vertex v has two orbits on the neighborhood of v. In this paper, such graphs of order at most 150 with the basic cycles of prime length are investigated, and a classification is given for such graphs which are non-Cayley graphs, whose block graphs induced by the basic cycles are non-bipartite graphs.

Properties of Classes of Random Graphs

1994 ◽  
Vol 3 (4) ◽  
pp. 435-454 ◽  
Author(s):  
Neal Brand ◽  
Steve Jackson
Keyword(s):  
Random Graphs ◽  
Higher Order ◽  
Order Property ◽  
First Order ◽  
New Class ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Almost All ◽  
Transitive Graphs

In [11] it is shown that the theory of almost all graphs is first-order complete. Furthermore, in [3] a collection of first-order axioms are given from which any first-order property or its negation can be deduced. Here we show that almost all Steinhaus graphs satisfy the axioms of almost all graphs and conclude that a first-order property is true for almost all graphs if and only if it is true for almost all Steinhaus graphs. We also show that certain classes of subgraphs of vertex transitive graphs are first-order complete. Finally, we give a new class of higher-order axioms from which it follows that large subgraphs of specified type exist in almost all graphs.

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