A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
On edge-Hamiltonian property of Cayley graphs
1988
Discrete Mathematics
Preserved Fulltext
Hence every Cayley graph of order a power of 2 is edge-Hamiltonian. ...
A Cayley graph ouer G is defined as a graph G(X) whose vertex set is G and whose edge set consists of all unordered pairs [a, b] with a, b E G and am'b E X U X-', where X-t denotes the set (x-t ( .x E ...
Edge Hamiltonian property of Cayley graphs With the basic lemmas established in the previous section, we are now in a position to prove the following theorems.
Theorem 5. ...
doi:10.1016/0012-365x(88)90191-4
fatcat:h2mvnqlj4ncwre3s56jvnonyve
On edge-hamiltonian Cayley graphs
1994
Discrete Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Chen (1988) conjectured that every finite hamiltonian Cayley graph is edge-hamiltonian. We prove some hamiltonian Cayley graphs to be edge-hamiltonian and some Cayley graphs to be hamiltonian. ...
Results of Alspach and Zhang (1989) on Hamilton cycles in Cayley graphs on dihedral groups are generalized. 0166-218X/94/$07.00 0 199LElsevier Science B.V. ...
Edge-hamiltonian property of Cayley graphs In investigating whether a given hamiltonian Cayley graph has the property that each of its edges lies on a Hamilton cycle, the following result of Chen can be ...
doi:10.1016/0166-218x(94)90091-4
fatcat:4uxp7nbk7zbi3dwhxmqcdtcqxq
Hamiltonian decomposition of Cayley graphs of degree 4
1989
Journal of combinatorial theory. Series B (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We prove that any 4-regular connected Cayley graph on a finite abelian group can be decomposed into two hamiltonian cycles. ...
This answers a partial case of Alspach's conjecture concerning hamiltonian decompositions of 2k-regular connected Cayley graphs. ...
Such a property is interesting because routings on a hamiltonian cycle are easy; these graphs are good fault-tolerant networks because in case of edge failure one can always find a simple routing. ...
doi:10.1016/0095-8956(89)90040-3
fatcat:huxfuaizhrdojbly4new3v6xre
An evidence for Lov´asz conjecture about Hamiltonian paths and cycles
2010
Matemática contemporânea
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
In this work, we show some properties of the gadget graph H l,p which was used by Holyer to prove the NP−completeness of the problem of the edge-partition into cliques [3] . ...
However, since none of these four graphs is a Cayley graph, we can look at the Lovász conjecture as stating that every connected Cayley graph with more than two vertices has a Hamiltonian cycle. ...
The graph H l,p has the following properties: 1. the degree of each vertex is 2( l 2 );
the number of vertices is p l−1 ; 3. the number of edges is ( l 2 )p l−1 . ...
doi:10.21711/231766362010/rmc3914
fatcat:as4bgm3waba35eon5x332oafva
Page 3572 of Mathematical Reviews Vol. , Issue 91G
[page]
1991
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
A graph G whose square G* is Hamiltonian is called a critical graph if the removal of any edge of G results in a graph whose square is not Hamiltonian. ...
In this paper, the authors give a sufficient condition for Cayley digraphs to have Hamiltonian circuits, and give a lower bound on the number of Hamiltonian circuits in a Hamiltonian Cayley digraph. ...
Hamiltonian Decomposition of Recursive Circulants
[chapter]
1998
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
The result is not only a partial answer to the problem posed by Alspach that every connected Cayley graph over an abelian group is hamiltonian decomposable, but also an extension of Micheneau's that recursive ...
We show that recursive circulant G(cd m ; d) is hamiltonian decomposable. Recursive circulant is a graph proposed for an interconnection structure of multicomputer networks in 8]. ...
Graph classes Hamiltonian decomposition is one of the most interesting strong hamiltonicity, that is, a hamiltonian property which implies the existence of a hamiltonian cycle. ...
doi:10.1007/3-540-49381-6_32
fatcat:c7dww2hcyfh4dkip4zj3sq25q4
Approximating Cayley diagrams versus Cayley graphs
[article]
2011
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. ...
We give an example where this subtree is a Hamiltonian cycle, but convergence is meant in a stronger sense. These latter are related to whether having a Hamiltonian cycle is a testable graph property. ...
The other sequence, K n will also be the direct product of a graph B n and C 4 , and it will have the property that it contains a Hamiltonian cycle such that every other edge of the Hamiltonian cycle is ...
arXiv:1103.4968v3
fatcat:q5djorgymreo3fvojrpanbffq4
On the structure of Hamiltonian cycles in Cayley graphs of finite quotients of the modular group
1998
Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
It is a fairly longstanding conjecture that if G is any finite group with IG/ > 2 and if X is any set of generators of G then the Cayley graph T(G : X) should have a Hamiltonian cycle. ...
It turns out that in the case where G is a finite quotient of the modular group the Hamiltonian cycles possess remarkable structural properties. ...
I am particularly grateful to Nigel Boston for his patience in showing me how to use the computer algebra system CAYLEY and its successor MAGMA. ...
doi:10.1016/s0304-3975(98)00041-3
fatcat:732oc4jdpzfzxjtib56e4kpj34
Embeddings on Torus-Butterfly Interconnection Network
2012
International Journal of Applied Information Systems
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
From the properties of Cayley graphs which have Hamiltonian path, the linear array and 2D-Mesh can be embedded into this new Torus-Butterfly network with minimum dilation and expansion. ...
Torus-Butterfly network is a Cayley graph. ...
As already mentioned in the introduction, one of the models that are widely used as interconnection networks are Cayley graphs, this is caused by the Cayley graph has the properties finite, connect, undirected ...
doi:10.5120/ijais12-450817
fatcat:l3cwgx65fbf2xecu7whq4w3eou
Hamiltonian decompositions of 4-regular Cayley graphs of infinite abelian groups
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
A well-known conjecture of Alspach says that every 2k-regular Cayley graph of an abelian group can be decomposed into Hamiltonian cycles. ...
In this setting one natural analogue of a Hamiltonian cycle is a spanning double-ray. ...
Let G be a locally finite graph. Then a set of edges C is a circle if and only if C meets every finite cut F of G in an even number of edges, and there is no non-empty C ′ C with this property. ...
arXiv:2006.09759v1
fatcat:dok7hkzr4vewppoduc36rscuam
Page 3282 of Mathematical Reviews Vol. , Issue 85h
[page]
1985
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
one edge between them, then G is Hamiltonian. ...
We thereby make use of the algebraic properties of G to establish that at least one of a pair of cycles can be lifted appropriately.”
Pareek, C. M. (KWT-KUWA); Skupien, Z. ...
Some problems on Cayley graphs
2008
Linear Algebra and its Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
This survey paper presents the historical development of some problems on Cayley graphs which are interesting to graph and group theorists such as Hamiltonicity or diameter problems, to computer scientists ...
Acknowledgments I thank Reza Khosrovshahi for inviting me to participate at the First IPM (Institute for Studies in Theoretical Physics and Mathematics) conference on Algebraic Graph Theory that was held ...
on April 21-26, 2007, in Tehran and for his hospitality during my staying in Iran. ...
doi:10.1016/j.laa.2008.05.010
fatcat:aw4jerefane77kfhanjxqeivvi
Page 2608 of Mathematical Reviews Vol. , Issue 96e
[page]
1996
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
)
The Hamiltonian property of Cayley graphs on symmetric groups. ...
Sci. 11 (1994), no. 3, 16-18.
05 COMBINATORICS
2608
96e:05074b 05C25 05C45 20B30
Wang, Shi Ying [Wang, Shi Ying”] (PRC-XINJ-EM; Urumgi)
The Hamiltonian property of Cayley graphs on symmetric groups. ...
Biswapped Networks and Their Topological Properties
2007
Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2010; you can also visit the original URL.
The file type is application/pdf.
We show how key parameters of a BSN are related to the corresponding parameters of its basis network and obtain a number of results on internode distances, Hamiltonian cycles, and node-disjoint paths. ...
In particular, if the basis network is a Cayley digraph then so is the resulting BSN. ...
Acknowledgment Research of the first four authors was supported by the Natural Science Foundation of China and Guangdong Province (No.04020130). ...
doi:10.1109/snpd.2007.217
dblp:conf/snpd/XiaoCHWP07
fatcat:o4pdvrfxb5b4lenkdmddq6ytii
Hamiltonian paths in Cayley graphs
2009
Discrete Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
In Section 4 we try to emphasize the group theoretic and algebraic combinatorial properties of Cayley graphs. ...
Here we present a construction of Hamiltonian 3-regular Cayley graphs, and prove that these are expanders. ...
We shall ignore labels and orientation of edges and treat Γ as a simple graph on |G| vertices. Clearly, Γ is d-regular, where d = |S|. From this point on, we consider only Cayley graphs. ...
doi:10.1016/j.disc.2009.02.018
fatcat:efhn3mkayzgl3hsvpljbcyoe3y
« Previous
Showing results 1 — 15 out of 1,925 results