Moore graphs and beyond: a survey of the degree/diameter problem.
Miller, Mirka, Širáň, Jozef (2005)
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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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.
Zofia Majcher, Jerzy Michael (1998)
Discussiones Mathematicae Graph Theory
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A digraph such that for each its vertex, vertices of the out-neighbourhood have different in-degrees and vertices of the in-neighbourhood have different out-degrees, will be called an HI-digraph. In this paper, we give a characterization of sequences of pairs of out- and in-degrees of HI-digraphs.
Stanislav Jendrol′, Mária Maceková, Mickaël Montassier, Roman Soták (2016)
Discussiones Mathematicae Graph Theory
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In this paper we study the existence of unavoidable paths on three vertices in sparse graphs. A path uvw on three vertices u, v, and w is of type (i, j, k) if the degree of u (respectively v, w) is at most i (respectively j, k). We prove that every graph with minimum degree at least 2 and average degree strictly less than m contains a path of one of the types [...] Moreover, no parameter of this description can be improved.
Philip J. Pratt, Donald W. Vanderjagt (1977)
Colloquium Mathematicae
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Liskovets, Valery A. (2000)
Journal of Integer Sequences [electronic only]
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Zyta Dziechcińska-Halamoda, Zofia Majcher, Jerzy Michael, Zdzisław Skupień (2007)
Discussiones Mathematicae Graph Theory
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Digraphs in which ordered pairs of out- and in-degrees of vertices are mutually distinct are called irregular, see Gargano et al. [3]. Our investigations focus on the problem: what are possible sizes of irregular digraphs (oriented graphs) for a given order n? We show that those sizes in both cases make up integer intervals. The extremal sizes (the endpoints of these intervals) are found in [1,5]. In this paper we construct, with help of Sokoban-type game, n-vertex irregular oriented...
Shariefuddin, Pirzada, Merajuddin, Pirzada (1996)
Novi Sad Journal of Mathematics
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Šiagiová, J. (2002)
Acta Mathematica Universitatis Comenianae. New Series
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D. G. Akka, J. K. Bano (2001)
Mathematica Bohemica
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In this paper, we present characterizations of pairs of graphs whose join graphs are 2-minimally nonouterplanar. In addition, we present a characterization of pairs of graphs whose join graphs are 2-minimally nonouterplanar in terms of forbidden subgraphs.