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Most direct product of graphs are Type 1
[article]

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 ...

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

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. ...

##
###
Walk-based Graph Kernel for Drug Discovery: A Review

2014
*
International Journal of Computer Applications
*

There

doi:10.5120/16440-5878
fatcat:cvy6pp2qyngfzl3oypvojq6rzu
*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. ...##
###
On modeling building evacuation route plans by resorting to P-graph

2011
*
Revista Colombiana de Computación
*

This paper presents basic ideas on the application

doaj:0c05158bc5ce4dbfaa02b467d45f0567
fatcat:zxi36exre5djxnlou4eyh5swie
*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. ...##
###
Constructing VEGGIE: Machine Learning for Context-Sensitive Graph Grammars

2007
*
19th IEEE International Conference on Tools with Artificial Intelligence(ICTAI 2007)
*

However, the high dimensionality

doi:10.1109/ictai.2007.59
dblp:conf/ictai/AtesZ07
fatcat:hxb5d4a2hzcwlpiy3lumlnsbm4
*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. ...##
###
Attributed graph transformation with node type inheritance

2007
*
Theoretical Computer Science
*

These

doi:10.1016/j.tcs.2007.02.001
fatcat:3zzyt7hacbcsrbjiizn4ebg3v4
*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 ...##
###
Bipartite and directed scale-free complex networks arising from zeta functions

2014
*
Communications in nonlinear science & numerical simulation
*

We construct a new class

doi:10.1016/j.cnsns.2013.08.037
fatcat:czpy2btafrhwbcqyhlmlqlc7gq
*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. ...##
###
Snarks with total chromatic number 5

2015
*
Discrete Mathematics & Theoretical Computer Science
*

Cubic

doi:10.46298/dmtcs.2111
fatcat:ghmwdb4ykfbsddtzxayit6qswq
*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. ...##
###
Faster isometric embedding in products of complete graphs

1994
*
Discrete Applied Mathematics
*

We also show that an n-vertex subgraph

doi:10.1016/0166-218x(94)90154-6
fatcat:2zmf7fc5nfg3xb453lghokaopq
*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*. ...##
###
Large graphs with given degree and diameter. II

1984
*
Journal of combinatorial theory. Series B (Print)
*

Then G * C,,, where &X,Yj(x') = 3x' (mod 17) if (x, y) is

doi:10.1016/0095-8956(84)90012-1
fatcat:ch2rvg7w4rgirj2fafyibfo5ji
*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. ...##
###
The enumeration of planar graphs via Wick's theorem

2009
*
Advances in Mathematics
*

We express the number

doi:10.1016/j.aim.2009.03.001
fatcat:63vx2uuuyvdzpdeagbvjpyrhwy
*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). ...##
###
The enumeration of planar graphs via Wick's theorem
[article]

2009
*
arXiv
*
pre-print

We express the number

arXiv:math/0605218v3
fatcat:d6m6lcfodbffzboe5s7r3zifbi
*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*). ...##
###
On Large-Scale Graph Generation with Validation of Diverse Triangle Statistics at Edges and Vertices

2018
*
2018 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)
*

Such

doi:10.1109/ipdpsw.2018.00056
dblp:conf/ipps/SandersPFK18
fatcat:hi2fia6mpnaylaiskdt5jfxnxu
*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] . ...##
###
Patterns of Influence in a Recommendation Network
[chapter]

2006
*
Lecture Notes in Computer Science
*

We enumerate and count cascade subgraphs on large

doi:10.1007/11731139_44
fatcat:hjb2wztyg5bmbhxlffwia35gna
*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. ...##
###
Unfolding and Event Structure Semantics for Graph Grammars
[chapter]

1999
*
Lecture Notes in Computer Science
*

This results, besides con rming the appropriateness

doi:10.1007/3-540-49019-1_6
fatcat:whqurgtww5atbp6zrj7f7e4g6e
*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. ...
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