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Solving computational problems in the theory of word-representable graphs
[article]

2018
*
arXiv
*
pre-print

A simple

arXiv:1808.01215v1
fatcat:yzl3vjtnajce3jxyi2g4nxwyna
*graph*G=(V,E) is*word*-*representable*if there exists a*word*w over*the*alphabet V such that letters x and y alternate*in*w iff xy∈ E. ... Our*computational*results*in*this paper not only include distribution*of*k-*representable**graphs*on at most 9 vertices, but also have relevance to a known conjecture on these*graphs*. ...*The*roots*of**the**theory**of**word*-*representable**graphs*are*in**the*study*of**the*celebrated Perkins semigroup*in*[23] , which has played a central role*in*semigroup*theory*since 1960, particularly as a source ...##
###
Foreword to the Special Focus on Graph Theory and Applications

2016
*
Mathematics in Computer Science
*

It is

doi:10.1007/s11786-016-0272-2
fatcat:hi2elo6prrb53l2m2wlhot43sa
*the*Swiss mathematician Euler who is credited for having introduced*the*concept*of*a*graph**in**solving**the*famous bridge*problem*. ... interactions with experts*in**the*field*of**graph**theory*,*the*School*of**Computer*Science at Universiti Sains Malaysia, Penang organised an International Workshop on*Graph*Algorithms (IWGA)*in*May 2015. ...*The*paper by Mahmood and others deals with one*of**the*main*problems**of*algorithmic*graph**theory*, called minimum dominating set*in*a*graph*. ...##
###
THE REAL-WORLD-SEMANTICS INTERPRETABILITY OF LINGUISTIC RULE BASES AND THE APPROXIMATE REASONING METHOD OF FUZZY SYSTEMS

2019
*
Vietnam Journal of Science and Technology
*

assigning

doi:10.15625/2525-2518/57/2/13129
fatcat:n6z2i56krzf4vermtaxuc473fa
*computational*objects*in**the*appropriate*computational*structure to*the**words*so that*the*relationships between*the**computational*semantics*in**the**computational*structure is*the*image*of*relationships ... to construct*computational*semantics*of*linguistic*words*so that a method developed based on handling*the**computational*semantics*of*linguistic terms to simulate a human method immediately handling*words*... This research is funded by Vietnam Academy*of*Science and Technology (VAST) under Grant No. VAST01.07/17-18.*The*authors gratefully acknowledge reviewers' comments improving better*the*paper. ...##
###
Computer-Based Instruction on Multimedia Networking Fundamentals: Equational Versus Graphical Representation

2005
*
IEEE Transactions on Education
*

*In*this paper, they describe

*the*design and development

*of*

*the*module, which is aligned with Gagne's

*theory*

*of*instruction. ... They have developed two versions

*of*

*the*module-one with equation-based

*representation*

*of*

*the*learning content and one with

*graph*-based

*representation*

*of*

*the*learning content. ...

*representation*by an equation-

*word*combination and a

*graph*-

*word*combination. ...

##
###
Logspace computations in graph products
[article]

2014
*
arXiv
*
pre-print

We consider three important and well-studied algorithmic

arXiv:1309.1290v3
fatcat:ynglwr6sbnbfbgdt72z7gtd47q
*problems**in*group*theory*:*the**word*, geodesic, and conjugacy*problem*. We show transfer results from individual groups to*graph*products. ... We have a general result for*graph*products, but even*in**the*special case*of*a*graph*group*the*result is new. ... Assume that*the**word**problem**of*P and B can be*solved**in*logspace and that*the*membership*problem*for A*in*P can be*solved**in*logspace, too. Then*the**word**problem**of*G can be*solved**in*logspace. ...##
###
Page 1594 of Mathematical Reviews Vol. , Issue 93c
[page]

1993
*
Mathematical Reviews
*

*The*subgraph and

*the*auxiliary structure are used to construct

*the*tree

*representation*

*of*

*the*original

*graph*

*in*linear time. ... Finally, we show that when locations

*of*Steiner points are not fixed

*the*

*problem*remains NP-complete; however, if

*the*topology

*of*

*the*final tree is given, then

*the*prob- lem can be

*solved*

*in*©(|p|log|p ...

##
###
Page 5983 of Mathematical Reviews Vol. , Issue 94j
[page]

1994
*
Mathematical Reviews
*

*The*variable membership

*problem*for GCSGs is shown to be NP-complete. This

*solves*a

*problem*posed by E. Dahlhaus and M. K. Warmuth [J.

*Comput*. System Sci. 33 (1986), no. 3, 456-472; MR 88e:68058]. ... Term

*graph*rewriting addresses

*the*

*problem*

*of*representing terms and term-rewrite rules as

*graphs*and

*graph*-rewrite rules. ...

##
###
Identification of Graph Thinking in Solving Mathematical Problems Naturally

2022
*
Participatory Educational Research
*

and have flexibility

doi:10.17275/per.22.32.9.2
fatcat:umegho52rfd3zlimrp42j66iom
*in**solving*a*problem*. These skills are urgently needed*in**the*21st century where rapid and continuous changes occur. ... Acknowledgements*The*researchers would like to thank*the*Endowment Fund for Education (LPDP) for its scholarship, BUDI-DN. ... Meanwhile,*the*study conducted by Csíkos et al. (2012) indicates*the*importance*of*visual*representations**in*mathematics modelling*in**solving**word**problems*. ...##
###
Page 4076 of Mathematical Reviews Vol. , Issue 80J
[page]

1980
*
Mathematical Reviews
*

*In*this paper some general results are established and a large class

*of*properties is defined for which

*the*corresponding c.n.d.

*problem*is difficult to

*solve*. ... We determine explicitly

*the*com- plexity

*of*a general pair

*of*bilinear forms

*in*terms

*of*parameters related to Kronecker’s

*theory*

*of*pencils and to

*the*

*theory*

*of*invariant polynomials. ...

##
###
Preface of STACS 2012 Special Issue

2014
*
Theory of Computing Systems
*

Improving

doi:10.1007/s00224-013-9530-8
fatcat:735tiimi7jax7nxaupttepgxlu
*the*bound*of*a circulation*in*a network arising*in**the*analysis, he succeeds to show*the*ratio 13/9 for*the*TSP and*the*ratio 19/12 for*the*traveling salesman path*problem**in*graphic metrics. ...*The*article 13/9-approximation for*the*Graphic TSP by Marcin Mucha improves*the*analysis*of*an approximation algorithm for*the*traveling salesman*problem*(TSP) for graphic metrics, which received considerable ... His main result consists*in*proving that, from*the*level 3 on,*the*first-order*theory**of**the**computation**graphs**of*collapse pushdown automata, is undecidable. ...##
###
Incremental Symmetry Breaking Constraints for Graph Search Problems

2020
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

This facilitates a "generate and extend" paradigm for parallel

doi:10.1609/aaai.v34i02.5513
fatcat:5xzcxod4wvdhpju3pgb2s2bg7q
*graph*search*problem**solving*: To*solve*a*graph*search*problem*φ on order n*graphs*, first generate*the*canonical*graphs**of*some order k < n ... Then,*compute*canonical solutions for φ by extending,*in*parallel, each canonical order k*graph*together with suitable symmetry breaking constraints. ... We acknowledge*the*support*of**the*Israel Science Foundation, grant 625/17. ...##
###
Graph theory representations of engineering systems and their embedded knowledge

1999
*
Artificial Intelligence in Engineering
*

*The*discrete mathematical

*representations*

*of*

*graph*

*theory*, augmented by theorems

*of*matroid

*theory*, were found to have elements and structures isomorphic with those

*of*many different engineering systems ... Using various

*graph*

*representations*and

*the*theorems and algorithms embedded within them, provides a fruitful source

*of*

*representations*which can form a basis upon which to extend formal

*theories*

*of*reformulation ... Gurion University

*of*

*the*Negev. ...

##
###
Page 5121 of Mathematical Reviews Vol. , Issue 911
[page]

1991
*
Mathematical Reviews
*

Summary: “Modular decomposition is a form

*of**graph*decom- position that has been discovered independently by researchers*in**graph**theory*, game*theory*, network*theory*, and other areas. ...*Comput*. 14 (1985), no. 3, 658-670], this leads to fast new algorithms for a number*of**problems**in**graph*recognition and isomorphism, including recognition*of*comparability*graphs*and permutation*graphs*...##
###
Studies on Dimultigraph and Prograph Based Applications of Graph Theory in Computer Science

2010
*
International journal of computer and communication technology
*

*Graph*

*Theory*has gained an impulsion

*in*

*the*past few years

*in*rapacious dimensions. ... And many seemingly diverse

*problems*

*in*

*computer*science have been worked out with

*the*help

*of*this thought. ... Consequently,

*graphs*are extremely important

*in*

*Computer*Science mainly for

*the*reasons: a. Without

*graphs*,

*representations*

*of*many

*problems*

*in*

*computer*science become abstract. b. ...

##
###
Guest editorial: special issue on data mining with matrices, graphs and tensors

2011
*
Data mining and knowledge discovery
*

*In*these methods,

*the*data is described using matrix

*representations*(

*graphs*are represented by their adjacency matrices) and

*the*data mining

*problem*is formulated as an optimization

*problem*with matrix ...

*The*field

*of*data mining increasingly adapts methods and algorithms from advanced matrix

*computations*,

*graph*

*theory*and optimization. ... Geoff Webb for his great help and support

*in*organizing

*the*issue. ...

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