Graphs having planar complementary line (total) graphs.
Simic, Slobodan K. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Simic, Slobodan K. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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V.R. Kulli, B. Basavanagoud (2004)
Discussiones Mathematicae Graph Theory
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In this paper we present characterizations of graphs whose plick graphs are planar, outerplanar and minimally nonouterplanar.
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.
Steve Fisk (1995)
Discussiones Mathematicae Graph Theory
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A homomorphism from one graph to another is a map that sends vertices to vertices and edges to edges. We denote the number of homomorphisms from G to H by |G → H|. If 𝓕 is a collection of graphs, we say that 𝓕 distinguishes graphs G and H if there is some member X of 𝓕 such that |G → X | ≠ |H → X|. 𝓕 is a distinguishing family if it distinguishes all pairs of graphs. We show that various collections of graphs are a distinguishing family.
Peter Hudák, Mária Maceková, Tomáš Madaras, Pavol Široczki (2016)
Discussiones Mathematicae Graph Theory
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A graph H is defined to be light in a graph family 𝒢 if there exist finite numbers φ(H, 𝒢) and w(H, 𝒢) such that each G ∈ 𝒢 which contains H as a subgraph, also contains its isomorphic copy K with ΔG(K) ≤ φ(H, 𝒢) and ∑x∈V(K) degG(x) ≤ w(H, 𝒢). In this paper, we investigate light graphs in families of plane graphs of minimum degree 2 with prescribed girth and no adjacent 2-vertices, specifying several necessary conditions for their lightness and providing sharp bounds on φ and w...
Jaroslav Ivanco (2007)
Discussiones Mathematicae Graph Theory
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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.
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.
Yan Yang, Yichao Chen (2017)
Discussiones Mathematicae Graph Theory
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The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study...
Július Czap, Jakub Przybyło, Erika Škrabuľáková (2016)
Discussiones Mathematicae Graph Theory
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A graph G = (V, E) is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite 1-planar graphs with prescribed numbers of vertices in partite sets. Bipartite 1-planar graphs are known to have at most 3n − 8 edges, where n denotes the order of a graph. We show that maximal-size bipartite 1-planar graphs which are almost balanced have not significantly fewer edges than indicated by this upper bound, while the same...
Isaak, Garth, West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Benjamin S. Baumer, Yijin Wei, Gary S. Bloom (2016)
Discussiones Mathematicae Graph Theory
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Suppose that G is a simple, vertex-labeled graph and that S is a multiset. Then if there exists a one-to-one mapping between the elements of S and the vertices of G, such that edges in G exist if and only if the absolute difference of the corresponding vertex labels exist in S, then G is an autograph, and S is a signature for G. While it is known that many common families of graphs are autographs, and that infinitely many graphs are not autographs, a non-autograph has never been exhibited....
Gutman, I. (1996)
Publications de l'Institut Mathématique. Nouvelle Série
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Caro, Yair, West, Douglas B. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Dragoš Cvetković, Tatjana Davidović (2009)
Zbornik Radova
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Bagga, Jay (2004)
International Journal of Mathematics and Mathematical Sciences
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