scholarly journals On super 2-restricted and 3-restricted edge-connected vertex transitive graphs

2011 ◽  
Vol 311 (23-24) ◽  
pp. 2683-2689 ◽  
Author(s):  
Weihua Yang ◽  
Zhao Zhang ◽  
Chengfu Qin ◽  
Xiaofeng Guo
Keyword(s):  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs ◽  
Connected Vertex

scholarly journals Hamiltonian paths in odd graphs

2009 ◽  
Vol 3 (2) ◽  
pp. 386-394 ◽  
Author(s):  
Letícia Bueno ◽  
Luerbio Faria ◽  
Figueiredo De ◽  
Fonseca Da
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Transitive Graph ◽  
Direct Computation ◽  
Hamiltonian Paths ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Vertex Transitive Graph ◽  
Transitive Graphs ◽  
Connected Vertex

Lov?sz conjectured that every connected vertex-transitive graph has a Hamiltonian path. The odd graphs Ok form a well-studied family of connected, k-regular, vertex-transitive graphs. It was previously known that Ok has Hamiltonian paths for k ? 14. A direct computation of Hamiltonian paths in Ok is not feasible for large values of k, because Ok has (2k - 1, k - 1) vertices and k/2 (2k - 1, k - 1) edges. We show that Ok has Hamiltonian paths for 15 ? k ? 18. Instead of directly running any heuristics, we use existing results on the middle levels problem, therefore further relating these two fundamental problems, namely finding a Hamiltonian path in the odd graph and finding a Hamiltonian cycle in the corresponding middle levels graph. We show that further improved results for the middle levels problem can be used to find Hamiltonian paths in Ok for larger values of k.

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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