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Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs And Line Splitting Graphs

2010
*
Mapana Journal of Sciences
*

For a

doi:10.12723/mjs.17.7
fatcat:tlnsbzayl5fpre7jobeqju3oxm
*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. ...##
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Interaction graphs: Graphings

2017
*
Annals of Pure and Applied Logic
*

This third paper extends this approach by considering a generalization of

doi:10.1016/j.apal.2016.10.007
fatcat:w73giez5ufbljk34qoqh7rp66q
*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*. ...##
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Graph equations for line graphs, total graphs, middle graphs and quasi-total graphs

1984
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Discrete Mathematics
*

The authors are also thankful to the referee for suggesting the name 'quasi-total

doi:10.1016/0012-365x(84)90137-7
fatcat:tjxddt2liffephrgb3i746bk2y
*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. ...##
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Interaction Graphs: Graphings
[article]

2015
*
arXiv
*
pre-print

This third paper extends this approach by considering a generalization of

arXiv:1405.6331v3
fatcat:kludemw6kneynbsdls7hswvjri
*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*. ...##
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Equistable graphs, general partition graphs, triangle graphs, and graph products

2011
*
Discrete Applied Mathematics
*

*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*. ...

##
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γ-graphs of graphs

2011
*
Discussiones Mathematicae Graph Theory
*

, say D 1 and In this paper we initiate the study of γ-

doi:10.7151/dmgt.1562
fatcat:zgebnvr4qbgltm3stnjo7sv2vm
*graphs*of*graphs*. 518 2. ... In this paper we consider the family of all γ-sets in a*graph*G and we define the γ*graph*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 ′ . ...##
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Contracting Graphs to Split Graphs and Threshold Graphs
[article]

2013
*
arXiv
*
pre-print

In these problems we are given a

arXiv:1310.5786v1
fatcat:yqtmw2bh4rcbhh64x7rc7diyfy
*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. ...##
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Graphs and graph algorithms
[chapter]

2013
*
Scientific Programming
*

There is a wide range of computational tasks on

doi:10.1142/9789814513418_0018
fatcat:bfzcz6p7jzfv5bsd5hjxpr2ca4
*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). ...##
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Drawing Graphs Within Graphs

2005
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Journal of Graph Algorithms and Applications
*

This paper is based on a submission to the

doi:10.7155/jgaa.00097
fatcat:cmftyg3wqnf4binmo6c36nfcna
*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. ...##
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Fractal graph and integral graph: C-type hyper graph in graph theory

2019
*
Applied Mathematical Sciences
*

A new conception for C type hyper

doi:10.12988/ams.2019.812193
fatcat:xq4g4rxjebbmrchlh7mxl7glvm
*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. ...##
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Graphs isomorphic to their path graphs

2002
*
Mathematica Bohemica
*

Path

doi:10.21136/mb.2002.134066
fatcat:pbfnfmtqh5hspicao43lmzewru
*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. ...##
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Graph Coloring: Comparing Cluster Graphs to Factor Graphs
[article]

2021
*
arXiv
*
pre-print

In contrast to the prevalent literature that uses factor

arXiv:2110.02048v1
fatcat:nxjjz2wxpncbnb3gtd5v5monye
*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. ...##
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Small directed graphs as neighbourhood graphs

1988
*
Czechoslovak Mathematical Journal
*

Now consider the

doi:10.21136/cmj.1988.102221
fatcat:75hen5d34nc5fdu6fjt2rd7pzu
*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. ...##
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Graph equations for line graphs and total graphs

1975
*
Discrete Mathematics
*

Hence a complete

doi:10.1016/0012-365x(75)90054-0
fatcat:h2aemympmbg5ziip36gjr746te
*graph*. ... r disconmxted, In each of the possibilities mentioned above, it is easy to find corresponding*graphs*G and so eq. (2) iz; solved. ...##
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Biclique Graphs of K_3-free Graphs and Bipartite Graphs
[article]

2020
*
arXiv
*
pre-print

The biclique

arXiv:2006.00040v1
fatcat:guqiuq2j5vcahkrhvpltt3qr7y
*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. ...
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