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Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs And Line Splitting Graphs
2010
Mapana Journal of Sciences
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For a graph G, let G, L(G), J(G) S(G), L,(G) and M(G) denote Complement, Line graph, Jump graph, Splitting graph, Line splitting graph and Middle graph respectively. ...
The equality symbol '=' stands for on isomorphism between two graphs. ...
M(G)=L 5 (H) Beineke has shown in (2] that a graph G is a line graph if and only if G has none of the nine specified graphs f,, i = 1,2, .. . ,9 as an induced subgroph. ...
doi:10.12723/mjs.17.7
fatcat:tlnsbzayl5fpre7jobeqju3oxm
Interaction graphs: Graphings
2017
Annals of Pure and Applied Logic
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This third paper extends this approach by considering a generalization of graphs named graphings, which is in some way a geometric realization of a graph. ...
The strength of our approach lies in the fact that we interpret proofs by simpler structures -graphs -than Girard's constructions, while generalizing the latter since they can be recovered as special cases ...
We will here consider graphings as a generalization of graph or, more acutely, as a realization of a graph. ...
doi:10.1016/j.apal.2016.10.007
fatcat:w73giez5ufbljk34qoqh7rp66q
Graph equations for line graphs, total graphs, middle graphs and quasi-total graphs
1984
Discrete Mathematics
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The authors are also thankful to the referee for suggesting the name 'quasi-total graphs'. ...
Then we obtain a graph defined a graph M(G) as an intersection graph O(F) on the vertex-set V(G) of any graph G. ...
The solution of L(G)-~P(H) Beineke [2] has shown that a graph G is a line graph if and only if G has none of the nine specified graphs as an induced subgraph. ...
doi:10.1016/0012-365x(84)90137-7
fatcat:tjxddt2liffephrgb3i746bk2y
Interaction Graphs: Graphings
[article]
2015
arXiv
pre-print
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This third paper extends this approach by considering a generalization of graphs named graphings, which is in some way a geometric realization of a graph. ...
The strength of our approach lies in the fact that we interpret proofs by simpler structures - graphs - than Girard's constructions, while generalizing the latter since they can be recovered as special ...
We will here consider graphings as a generalisation of graph or, more acutely, as a realiser of a graph. ...
arXiv:1405.6331v3
fatcat:kludemw6kneynbsdls7hswvjri
Equistable graphs, general partition graphs, triangle graphs, and graph products
2011
Discrete Applied Mathematics
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graph is a general partition graph. ...
In this paper we examine the connections between equistable graphs, general partition graphs and triangle graphs. ...
: general partition graphs ⊆ strongly equistable graphs and equistable graphs ⊂ triangle graphs. ...
doi:10.1016/j.dam.2011.03.011
fatcat:mqsia6qonzddholqhcuwwkzcpm
γ-graphs of graphs
2011
Discussiones Mathematicae Graph Theory
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, say D 1 and In this paper we initiate the study of γ-graphs of graphs. 518 2. ...
In this paper we consider the family of all γ-sets in a graph G and we define the γgraph G(γ) = (V (γ), E(γ)) of G to be the graph whose vertices V (γ) correspond 1-to-1 with the γ-sets of G, and two γ-sets ...
Thus, the γ-graph of the graph G ′ is isomorphic to the tree T ′ . ...
doi:10.7151/dmgt.1562
fatcat:zgebnvr4qbgltm3stnjo7sv2vm
Contracting Graphs to Split Graphs and Threshold Graphs
[article]
2013
arXiv
pre-print
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In these problems we are given a graph G and an integer k and asked whether G can be modified into a split graph or a threshold graph, respectively, by contracting at most k edges. ...
We present an FPT algorithm for Split Contraction, and prove that Threshold Contraction on split graphs, i.e., contracting an input split graph to a threshold graph, is FPT when parameterized by the number ...
Threshold graphs constitute a subclass of both split graphs and interval graphs in graph theory. ...
arXiv:1310.5786v1
fatcat:yqtmw2bh4rcbhh64x7rc7diyfy
Graphs and graph algorithms
[chapter]
2013
Scientific Programming
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There is a wide range of computational tasks on graphs: Connectivity and components, Path-finding and traversals, including route finding, graph-searching, exhaustive cycles (Eulerian and Hamiltonian), ...
Embedding problems, eg planarity -embedding in the plane, Matching ('marriage problems'), graph colouring and partitioning, ...
There is a variety of different kinds of graphs: Undirected graphs, Directed graphs, Multi-graphs, Labelled graphs (either node-labelled, or edge-labelled, or both). ...
doi:10.1142/9789814513418_0018
fatcat:bfzcz6p7jzfv5bsd5hjxpr2ca4
Drawing Graphs Within Graphs
2005
Journal of Graph Algorithms and Applications
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This paper is based on a submission to the Graph Drawing Contest 2003 "Drawing Graphs within Graphs" [5] . ...
In this paper, we present an approach for drawing graphs within graphs that first produces a layout for the subgraphs thus increasing their locality. ...
Brandenburg, University of Passau, for the organization of the Graph Drawing Contest 2003 and for his constructive comments earlier versions of this paper. ...
doi:10.7155/jgaa.00097
fatcat:cmftyg3wqnf4binmo6c36nfcna
Fractal graph and integral graph: C-type hyper graph in graph theory
2019
Applied Mathematical Sciences
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A new conception for C type hyper graph is defined by fractal graph and integral graph in this paper. C type hyper graph is unified the general graph and C type hyper graph, i.e. any general graph ...
can be seen a integral graph from a C type hyper graph, and otherwise: any C type hyper graph can be seen a fractal graph from a general graph. ...
We call the graph on left is the integral graph of the fractal graph on right, and the graph on right is the fractal graph of the integral graph on left. ...
doi:10.12988/ams.2019.812193
fatcat:xq4g4rxjebbmrchlh7mxl7glvm
Graphs isomorphic to their path graphs
2002
Mathematica Bohemica
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Path graphs were investigated by Broersma and Hoede in [2] as a natural generalization of line graphs, since P 1 (G) is the line graph L(G) of G (for further connections to line graphs see [6] ). ...
Distance properties of path graphs are studied in [1] , [3] and [5] , and in [4] graphs with connected P 3 -path graphs are characterized. ...
doi:10.21136/mb.2002.134066
fatcat:pbfnfmtqh5hspicao43lmzewru
Graph Coloring: Comparing Cluster Graphs to Factor Graphs
[article]
2021
arXiv
pre-print
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2017
Proceedings of the ACM Multimedia 2017 Workshop on South African Academic Participation - SAWACMMM '17
unpublished
doi:10.1145/3132711.3132717 fatcat:4vngaxowqnbjncvzosvbynlnn4
doi:10.1145/3132711.3132717 fatcat:4vngaxowqnbjncvzosvbynlnn4
In contrast to the prevalent literature that uses factor graphs for this purpose, we instead approach it from a cluster graph perspective. ...
Our experiments indicate a significant advantage for preferring cluster graphs over factor graphs, both in terms of accuracy as well as computational efficiency. ...
the graph, and (d) a cluster graph configuration for this problem. ...
arXiv:2110.02048v1
fatcat:nxjjz2wxpncbnb3gtd5v5monye
Small directed graphs as neighbourhood graphs
1988
Czechoslovak Mathematical Journal
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Now consider the graphs without double edges. We shall determine the graphs G for particular graphs Я. If H is an empty graph, then G is any graph without edges. ...
The graph G 1]L is in Fig. 4 , the graph G 12 is in Fig. 5 , the graph G 13 is in Fig. 6 . The graph G 14 is the complete directed graph with four vertices. Fig. 3 . 3 Fig. 3. ...
doi:10.21136/cmj.1988.102221
fatcat:75hen5d34nc5fdu6fjt2rd7pzu
Graph equations for line graphs and total graphs
1975
Discrete Mathematics
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Hence a complete graph. ...
r disconmxted, In each of the possibilities mentioned above, it is easy to find corresponding graphs G and so eq. (2) iz; solved. ...
doi:10.1016/0012-365x(75)90054-0
fatcat:h2aemympmbg5ziip36gjr746te
Biclique Graphs of K_3-free Graphs and Bipartite Graphs
[article]
2020
arXiv
pre-print
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The biclique graph of a graph G, KB(G), defined as the intersection graph of the bicliques of G, was introduced and characterized in 2010. ...
We prove that KB(G) is the square graph of a particular graph which we call Mutually Included Biclique Graph of G (KB_m(G)). ...
The biclique graph of a graph G, denoted by KB(G), is the intersection graph of the bicliques of G. ...
arXiv:2006.00040v1
fatcat:guqiuq2j5vcahkrhvpltt3qr7y
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