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Most direct product of graphs are Type 1 [article]

Diane Castonguay and Celina M. H. de Figueiredo and Luis Antonio Kowada and Caroline Reis Patrão and Diana Sasaki
2021 arXiv   pre-print
Most classified direct product of graphs are Type 1.  ...  , except for C_4 × C_4, all direct product of cycle graphs C_m × C_n with m,n ≥ 3 are Type 1.  ...  Acknowledgements This work is partially supported by the Brazilian agencies CNPq (Grant numbers: 302823/2016-6, 407635/2018-1 and 313797/2020-0) and FAPERJ (Grant numbers: CNE E-26/202.793/2017 and ARC  ... 
arXiv:2110.14453v1 fatcat:othwnab6s5gbrm2bht34rdexti

A Note on an Old-Fashioned Algebra for (Disconnected) Graphs

Fabio Gadducci
2009 Electronical Notes in Theoretical Computer Science  
Graphs with interfaces are a simple and intuitive tool for allowing a graph G to interact with the environment, by equipping it with two morphisms J → G, I → G.  ...  ., containing only nodes connected to at most one edge.  ...  Acknowledgement I am indebted to Andrea Corradini, Aberto Lluch-Lafuente and Giacoma Valentina Monreale for the interesting discussions and the careful reading of the paper.  ... 
doi:10.1016/j.entcs.2009.10.014 fatcat:l2tzzbub4nestalgybcxjknyzi

Walk-based Graph Kernel for Drug Discovery: A Review

Preeja M.P., K P Soman
2014 International Journal of Computer Applications  
There are two different methods for virtual screening 1) structure based 2) ligand based.  ...  Based on the type of information, ligand based virtual screening can be performed in different ways. The machine learning approach using molecular graphs has been found to be very effective.  ...  There are four types of product graphs wherein direct product graph is used for walk kernel computation.  ... 
doi:10.5120/16440-5878 fatcat:cvy6pp2qyngfzl3oypvojq6rzu

On modeling building evacuation route plans by resorting to P-graph

Juan C. García Ojeda
2011 Revista Colombiana de Computación  
This paper presents basic ideas on the application of the P-graph framework for modeling building evacuation routes and computing the optimal one.  ...  To do so, P-graph relies on both combinatorial and graph techniques for facilitating such a work.  ...  University of Bucaramanga for their financial support.  ... 
doaj:0c05158bc5ce4dbfaa02b467d45f0567 fatcat:zxi36exre5djxnlou4eyh5swie

Constructing VEGGIE: Machine Learning for Context-Sensitive Graph Grammars

Keven Ates, Kang Zhang
2007 19th IEEE International Conference on Tools with Artificial Intelligence(ICTAI 2007)  
However, the high dimensionality of graph grammars result in costly effort for their construction and maintenance. Additionally, they are often error prone.  ...  As interest in applications for natural languages and data mining has increased, the machine learning of graph grammars poses a prime area of research.  ...  Department of Education.  ... 
doi:10.1109/ictai.2007.59 dblp:conf/ictai/AtesZ07 fatcat:hxb5d4a2hzcwlpiy3lumlnsbm4

Attributed graph transformation with node type inheritance

Juan de Lara, Roswitha Bardohl, Hartmut Ehrig, Karsten Ehrig, Ulrike Prange, Gabriele Taentzer
2007 Theoretical Computer Science  
These productions are equivalent to a number of concrete productions, resulting from the substitution of the abstract node types by the node types in their inheritance clan.  ...  The aim of this paper is to integrate typed attributed graph transformation with node type inheritance.  ...  Definition 4 (Graph Transformation) Given a (typed) graph production p = L l ←− K r −→ R A sequence G 0 ⇒ G 1 ⇒ ... ⇒ G n of direct (typed) graph transformations is called a (typed) graph transformation  ... 
doi:10.1016/j.tcs.2007.02.001 fatcat:3zzyt7hacbcsrbjiizn4ebg3v4

Bipartite and directed scale-free complex networks arising from zeta functions

Piergiulio Tempesta
2014 Communications in nonlinear science & numerical simulation  
We construct a new class of directed and bipartite random graphs whose topology is governed by the analytic properties of L-functions.  ...  The bipartite L-graphs and the multiplicative zeta graphs are relevant examples of the proposed construction. Phase transitions and percolation thresholds for our models are determined.  ...  Acknowledgments The research of P. T. has been partly supported by the grant FIS2011-00260, Ministerio de Ciencia e Innovación, Spain.  ... 
doi:10.1016/j.cnsns.2013.08.037 fatcat:czpy2btafrhwbcqyhlmlqlc7gq

Snarks with total chromatic number 5

Gunnar Brinkmann, Myriam Preissmann, Diana Sasaki
2015 Discrete Mathematics & Theoretical Computer Science  
Cubic graphs with χT = 4 are said to be Type 1, and cubic graphs with χT = 5 are said to be Type 2. Snarks are cyclically 4-edge-connected cubic graphs that do not allow a 3-edge-coloring.  ...  As neither Type 2 cubic graphs with girth at least 5 nor Type 2 snarks are known, this is taking two steps at once, and the two requirements of being a snark and having girth at least 5 should better be  ...  Acknowledgments This research was conducted using the resources of the Stevin supercomputer Infrastructure at Ghent University. Without these resources some results could not have been obtained.  ... 
doi:10.46298/dmtcs.2111 fatcat:ghmwdb4ykfbsddtzxayit6qswq

Faster isometric embedding in products of complete graphs

Franz Aurenhammer, Michael Formann, Ramana M. Idury, Alejandro A. Schäffer, Frank Wagner
1994 Discrete Applied Mathematics  
We also show that an n-vertex subgraph of (KJd, the Cartesian product of d cliques of size a, cannot have more than &(a -1)n log, n edges.  ...  An isometric embedding of a connected graph G into a Cartesian product of complete graphs is equivalent to a labeling of each vertex of G by a string of fixed length such that the distance in G between  ...  Most of the applications are especially concerned with the case where H, the codomain of the embedding, is the Cartesian product of complete graphs.  ... 
doi:10.1016/0166-218x(94)90154-6 fatcat:2zmf7fc5nfg3xb453lghokaopq

Large graphs with given degree and diameter. II

J.C Bermond, C Delorme, G Farhi
1984 Journal of combinatorial theory. Series B (Print)  
Then G * C,,, where &X,Yj(x') = 3x' (mod 17) if (x, y) is of type A and f&x') = 4x' (mod 17) if (x, y) is of type B, is a graph of diameter at most D + 2, maximum degree A + 2 on 17n vertices.  ...  arcs of type A or two arcs of direrent type A and B.  ... 
doi:10.1016/0095-8956(84)90012-1 fatcat:ch2rvg7w4rgirj2fafyibfo5ji

The enumeration of planar graphs via Wick's theorem

Mihyun Kang, Martin Loebl
2009 Advances in Mathematics  
We express the number of the graphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function.  ...  Some of the most puzzling conjectures of discrete mathematics are related to the notion of the cycle double cover.  ...  Martin Loebl gratefully acknowledges the support of CONICYT via grant Anillo en Redes ACT08. Mihyun Kang is supported by the Deutsche Forschungsgemeinschaft (DFG Pr. 296).  ... 
doi:10.1016/j.aim.2009.03.001 fatcat:63vx2uuuyvdzpdeagbvjpyrhwy

The enumeration of planar graphs via Wick's theorem [article]

Mihyun Kang, Martin Loebl
2009 arXiv   pre-print
We express the number of the graphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function.  ...  Some of the most puzzling conjectures of discrete mathematics are related to the notion of the cycle double cover.  ...  , e edges and ≤ N vertices, and E 1 (N, r, e), E 2 (N, r, e) are of type O(N −1 ).  ... 
arXiv:math/0605218v3 fatcat:d6m6lcfodbffzboe5s7r3zifbi

On Large-Scale Graph Generation with Validation of Diverse Triangle Statistics at Edges and Vertices

Geoffrey Sanders, Roger Pearce, Timothy La Fond, Jeremy Kepner
2018 2018 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)  
Such graphs are highly compressible: | E| edges are represented in O(| E|^1/2) memory and can be built in a distributed setting from small data structures, making them easy to share in compressed form.  ...  Here we show that many flavors of triangle participation can be cheaply calculated while generating a Kronecker product graph.  ...  Directed and Reciprocal Parts We use the most general directed graph model, where directed edges and reciprocal edges are treated differently [36] .  ... 
doi:10.1109/ipdpsw.2018.00056 dblp:conf/ipps/SandersPFK18 fatcat:hi2fia6mpnaylaiskdt5jfxnxu

Patterns of Influence in a Recommendation Network [chapter]

Jure Leskovec, Ajit Singh, Jon Kleinberg
2006 Lecture Notes in Computer Science  
We enumerate and count cascade subgraphs on large directed graphs; as one component of this, we develop a novel efficient heuristic based on graph isomorphism testing that scales to large datasets.  ...  We investigate a large person-to-person recommendation network, consisting of four million people who made sixteen million recommendations on half a million products.  ...  Cascades are ordered by size. 14 cascade patterns can be observed in all four product types; Table 2 includes 10 of them. The most common cascade, G 1 , represents a single recommendation.  ... 
doi:10.1007/11731139_44 fatcat:hjb2wztyg5bmbhxlffwia35gna

Unfolding and Event Structure Semantics for Graph Grammars [chapter]

Paolo Baldan, Andrea Corradini, Ugo Montanari
1999 Lecture Notes in Computer Science  
This results, besides con rming the appropriateness of our unfolding construction, unify the various event structure semantics for the DPO approach to graph transformation.  ...  computations of the original grammar.  ...  Acknowledgements The authors wish to thank Roberto Bruni and Fabio Gadducci for helpful discussions and the anonymous referees for their comments on the submitted version of this paper.  ... 
doi:10.1007/3-540-49019-1_6 fatcat:whqurgtww5atbp6zrj7f7e4g6e
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