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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1348429
Description: We investigate the existence of cycles of various lengths in connected Cayley graphs of valency at least 3 on generalized dihedral groups.
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1057755
Description: We prove that connected Cayley graphs of valency at least 3 on abelian groups are even edge-pancyclic and have cycles of every possible odd length bigger than or equal to the odd girth.
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1062931
Description: Let ex(n;t) denote the maximum number of edges in a graph G having order n without cycles of length t or less. We prove ex(23;8)=28,ex(24;8)=20 and ex(25;8)=30. Furthermore, we present new lower and u... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/937017
Description: A (δ, g)-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all (δ, g)-cages with odd girth g ≥ 9 are r-connected, where (r − 1)² ≤ δ + ... More
Reviewed: Reviewed
Date: 2011
Keyword: graph | girth | degree | cage
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1064345
Description: We examine the existing constructions of the smallest known vertex-transitive graphs of a given degree and girth 6. It turns out that most of these graphs can be described in terms of regular lifts of... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/928266
Description: A (k,g)-cage is a k-regular graph with girth g that has the fewest number of vertices. It has been conjectured (Fu et al., J Graph Theory 24 (1997), 187–191) that all (k,g)-cages are k-connected for k... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/921623
Description: In this paper, first we prove that any graph G is 2-connected if diam(G)≤g−1 for even girth g, and for odd girth g and maximum degree Δ≤2δ−1 where δ is the minimum degree. Moreover, we prove that any ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/932931
Description: A semiregular cage is a graph with degree set {r,r +1}, girth g and the smallest possible order. In this work we prove that semiregular cages with r ≥ 3 and odd girth g ≥ 7 are t-connected with t ≥ |√... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/808406
Description: By the extremal number ex(n;t) = ex(n;{C₃,C₄,…,Ct}) we denote the maximum size (number of edges) in a graph of n vertices, n > t, and girth (length of shortest cycle) at least g ≥ t + 1. In 1975, Erdő... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/916580
Description: A graph is superconnected, for short super-κ, if all minimum vertex-cuts consist of the vertices adjacent with one vertex. In this paper we prove for any r-regular graph of diameter D and odd girth g ... More
Reviewed: Reviewed
Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/41442
Description: A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G−X must have at least two ... More
Reviewed: Reviewed
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