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Clique graph representations of ptolemaic graphs
2010
Discussiones Mathematicae Graph Theory
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The first of these, called a clique tree representation, is easily generated from the clique graph of G (the intersection graph of the maximal complete subgraphs of G). ...
Thus, a ptolemaic graph G has two kinds of intersection graph representations: one from being chordal, and the other from being distance-hereditary. ...
Ptolemaic graphs therefore have two kinds of tree representations: both a clique tree because of being chordal, and a CC tree because of being distancehereditary. ...
doi:10.7151/dmgt.1520
fatcat:laqtj6bp3rcpziv2zmw3dixhr4
Vector representations of graphs
1989
Discrete Mathematics
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Various types of vector representations of graphs are related to Hadamard matrices, families of sets with prescribed intersections, and other combinatorial problems. ...
Let G be a simple graph with vertices 1,2, . . . , n. ...
Here we shall use Hadamard representations to prove that an interesting family of graphs is n-universal. ...
doi:10.1016/0012-365x(89)90171-4
fatcat:dsy5zsml5fgidiylqpkge2qzpy
Geometric representations of graphs
[chapter]
2010
Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization
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Consider an orthogonal representation i → v i ∈ R d of a graph G. ...
The skeleton of a polytope, as a representation of itself, is section-connected; and so is the rubber-band representation of a planar graph. ...
of the representing vectors. ...
doi:10.1090/fim/027/06
fatcat:hozttmgogzcv3epbax462axddy
Succinct representations of graphs
1983
Information and Control
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Hong (1980) gives an algorithm with this upper bound for a certain class of succinctly representable graphs. ...
The goals one would like to achieve by using a succinct representation are: (1) Reduce the amount of space required to store the graph. (2) Improve the complexity of certain graph algorithms. ...
doi:10.1016/s0019-9958(83)80004-7
fatcat:gw4uz4sy4zejnni4e6ebdhbtju
Representations of graphs modulon
1994
Journal of Graph Theory
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In particular, we relate the representation number of the disjoint union of complete graphs to the existence of complete families of mutually orthogonal Latin squares. ...
The representation number of graph G is the smallest n representing G. We review known results and investigate representation numbers for several new classes. ...
These tools will be used subsequently in determining representations and representation numbers of graphs and classes of graphs. ...
doi:10.1002/jgt.3190180805
fatcat:nvwjfxocdzbyziei6qokxnzbqy
Implicit representation of graphs
1988
Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88
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In the usual representations of an n-vertex graph, the names of the vertices (i.e. integers from 1 to n) betray nothing about the graph itself. ...
For example, we can label planar graphs with structure coding labels of size < 4 log n, which implies the existence of a graph with n 4 vertices that contains all n-vertex planar graphs as vertex induced ...
Furthermore from the representation of any graph it is easy to derive the representation of any of its vertex induced subgraphs. ...
doi:10.1145/62212.62244
dblp:conf/stoc/KannanNR88
fatcat:osg3ugvzvvhgbbmxq4mwv5be2u
Convex Representations of Graphs
1960
Proceedings of the London Mathematical Society
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Consider a convex representation R of a simple graph G in a plane IT, R being determined by a 1-1 mapping/of V(G) onto a set of points of IT. ...
We then call H a convex representation of G in E 2 . ...
doi:10.1112/plms/s3-10.1.304
fatcat:h2vb54d2mvdmhgbexk66xcxsd4
Orthogonal Representation of Graphs
[article]
2015
arXiv
pre-print
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Orthogonal Graph Representations are essential tools for testing existence of hidden variables in quantum theory. ...
Conducting experiments quantum contextuality or the information capacity of a quantum system are closely related to the orthogonal representations. ...
of the rest of the graph, so we reduce the dimension of the graph to n/2. ...
arXiv:1504.03662v2
fatcat:naveiodfl5bqtnqzde2jw3xorq
Geometric representations of graphs
1998
Computational geometry
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Geometric representations, or drawings, of graphs are widely used in information visualization applications, and their study has become increasingly popular in the last decade. ...
Research on graph drawing is being actively conducted from a variety of perspectives, including discrete mathematics, computational geometry, human-computer interaction, and computer graphics. ...
This special issue on Geometric Representations of Graphs contains five papers addressing a variety of graph drawing problems in two and three dimensions. ...
doi:10.1016/s0925-7721(97)00012-6
fatcat:ubv4vwlpibgizlvjcx2uurzhxi
Tree representations of graphs
2007
European journal of combinatorics (Print)
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A graph is chordal if and only if it is the intersection graph of some family of subtrees of a tree. Applying "tolerance" allows larger families of graphs to be represented by subtrees. ...
It is known that both [3, 3, 1] and [3, 3, 2] are equal to the family of chordal graphs. Furthermore, one can easily observe that every graph G belongs to [3, 3, t] for some t. ...
For h = 4, we get a (3, 3, 589)-representation of K n,n for every 590 ≤ n ≤ 3150. Hence we can set n 0 = 589. ...
doi:10.1016/j.ejc.2006.04.002
fatcat:tmurppq4knebrcvqamwpkpbigm
A plane graph representation of triconnected graphs
2010
Theoretical Computer Science
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graph in the plane. ...
Let G = (V , E) be a graph, S = {s 1 , s 2 , s 3 } be a set of three vertices of V , and assume that G has a directional S-embedding ψ. ...
the boundary B of H; (b) a region graph of the graph given inFig. 1(a). ...
doi:10.1016/j.tcs.2010.08.029
fatcat:2lknzogsa5gflgrio525xaoiiu
Graph representations of finite Abelian groups
1981
Czechoslovak Mathematical Journal
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If in the undirected graph representation of (5 each undirected edge xy is substituted by the pair of directed edges xy, yx, we obtain a directed graph representation of (6 c We shall study graph representations ...
For this undirected graph representation of © we can construct a directed graph representation of © in the way described in the proof of Proposition. ...
doi:10.21136/cmj.1981.101725
fatcat:r2oqa5avnrc7dprgy7yon6m5ci
Accurate Learning of Graph Representations with Graph Multiset Pooling
[article]
2021
arXiv
pre-print
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Yet, obtaining an accurate representation for a graph further requires a pooling function that maps a set of node representations into a compact form. ...
A simple sum or average over all node representations considers all node features equally without consideration of their task relevance, and any structural dependencies among them. ...
further encodes relationships between them to enhance the representation power of a graph. ...
arXiv:2102.11533v4
fatcat:qdqktuojbbbx7ofm6dgqzmevx4
Minimal Euclidean representations of graphs
[article]
2009
arXiv
pre-print
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In this note, we bound the Euclidean representation number of a graph using multiplicities of the eigenvalues of the adjacency matrix. ...
We also give an exact formula for the Euclidean representation number using the main angles of the graph. ...
This research is supported by NSERC, MITACS, PIMS, iCORE, and the University of Calgary Department of Mathematics and Statistics Postdoctoral Program. ...
arXiv:0812.3707v3
fatcat:usebhiv42fce3fpxe6uogxqzbe
A Characterization of Uniquely Representable Graphs
[article]
2020
arXiv
pre-print
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In this paper, we give a characterization of uniquely representable graphs by showing that they are exactly the block graphs. ...
A connected graph G is uniquely representable if there exists a unique metric betweenness structure with underlying graph G. It was implied by previous works that trees are uniquely representable. ...
Graphs that bound their representation from below and from above arise as the natural generalization of uniquely representable graphs. ...
arXiv:1708.01272v4
fatcat:mgaox6lufjeahblyhoc3kqjrxa
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