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A simple 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  , which has played a central role in semigroup theory since 1960, particularly as a source ...arXiv:1808.01215v1 fatcat:yzl3vjtnajce3jxyi2g4nxwyna
It is 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. ...doi:10.1007/s11786-016-0272-2 fatcat:hi2elo6prrb53l2m2wlhot43sa
Vietnam Journal of Science and Technology
assigning 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. ...doi:10.15625/2525-2518/57/2/13129 fatcat:n6z2i56krzf4vermtaxuc473fa
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. ...doi:10.1109/te.2005.849744 fatcat:36juluyqs5chxpubxo3jvsfgh4
We consider three important and well-studied algorithmic 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. ...arXiv:1309.1290v3 fatcat:ynglwr6sbnbfbgdt72z7gtd47q
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 ...
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. ...
and have flexibility 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. ...doi:10.17275/per.18.104.22.168 fatcat:umegho52rfd3zlimrp42j66iom
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. ...
Improving 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. ...doi:10.1007/s00224-013-9530-8 fatcat:735tiimi7jax7nxaupttepgxlu
This facilitates a "generate and extend" paradigm for parallel 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. ...doi:10.1609/aaai.v34i02.5513 fatcat:5xzcxod4wvdhpju3pgb2s2bg7q
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. ...doi:10.1016/s0954-1810(99)00002-3 fatcat:rvugl7kijfhzvfm2hqmd4m5n2a
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 ...
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. ...doi:10.47893/ijcct.2010.1039 fatcat:t7jug3qrtvgohgsi5b4wn7dymm
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. ...doi:10.1007/s10618-011-0214-1 fatcat:n4mf2ceoqzeitjdwq2opwtlm6e
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