A Moore-like bound for graphs of diameter 2 and given degree, obtained as abelian lifts of dipoles.
Šiagiová, J. (2002)
Acta Mathematica Universitatis Comenianae. New Series
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Šiagiová, J. (2002)
Acta Mathematica Universitatis Comenianae. New Series
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Lynne L. Doty (2011)
Discussiones Mathematicae Graph Theory
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For the notion of neighbor-connectivity in graphs whenever a vertex is subverted the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighbor-connectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is bounded above by κ. Doty has sharpened that bound in abelian Cayley graphs to approximately...
Caro, Yair, West, Douglas B. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Isaak, Garth, West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Carmi, Paz, Dujmovic, Vida, Morin, Pat, Wood, David R. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Miller, Mirka, Širáň, Jozef (2005)
The Electronic Journal of Combinatorics [electronic only]
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Yoshiharu Kohayakawa, Vojtěch Rödl, Mathias Schacht (2016)
Czechoslovak Mathematical Journal
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We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.
Ľudmila Bezegová, Jaroslav Ivančo (2012)
Discussiones Mathematicae Graph Theory
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A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2,..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+ |E(G)|)/2*deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.
Simic, Slobodan K. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Mekkia Kouider, Preben Dahl Vestergaard (2004)
Discussiones Mathematicae Graph Theory
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Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a,b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph.
Anna Fiedorowicz (2013)
Discussiones Mathematicae Graph Theory
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A k-colouring of a graph G is a mapping c from the set of vertices of G to the set {1, . . . , k} of colours such that adjacent vertices receive distinct colours. Such a k-colouring is called acyclic, if for every two distinct colours i and j, the subgraph induced by all the edges linking a vertex coloured with i and a vertex coloured with j is acyclic. In other words, every cycle in G has at least three distinct colours. Acyclic colourings were introduced by Gr¨unbaum in 1973, and since...
Xin Zhang, Yong Yu, Guizhen Liu (2011)
Open Mathematics
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A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.