Dynamic cage survey.
Exoo, Geoffrey, Jajcay, Robert (2008)
The Electronic Journal of Combinatorics [electronic only]
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Exoo, Geoffrey, Jajcay, Robert (2008)
The Electronic Journal of Combinatorics [electronic only]
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Gliviak, Ferdinand, Kyš, P. (1997)
Acta Mathematica Universitatis Comenianae. New Series
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V. A., Ustimenko (2007)
Serdica Journal of Computing
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We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed...
Petrović, Miroslav (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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Jaroslav Nešetřil (1978)
Mathematica Slovaca
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Vladislav Bína, Jiří Přibil (2015)
Commentationes Mathematicae Universitatis Carolinae
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The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split graphs.
A. K. Dewdney, Frank Harary (1976)
Czechoslovak Mathematical Journal
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Ashwin Ganesan (2016)
Discussiones Mathematicae Graph Theory
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Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also proved that the transposition graph T(S) is edge-transitive if and only if the Cayley graph Cay(Sn,...
Chandran, L.Sunil, Lozin, Vadim V., Subramanian, C.R. (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Cvetkovic, Dragos M. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Amanda Niedzialomski (2016)
Discussiones Mathematicae Graph Theory
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For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...