Top PDF Word Representability of Line Graphs

Word Representability of Line Graphs

Word Representability of Line Graphs

It was shown by Kitaev and Pyatkin, in [1], that if a graph is representable by , then one can assume that is uniform, that is, it contains the same number of copies of each letter. If the number of copies of each letter in is , we say that is -uniform. For example, the graph to the left in Figure 1 can be represented by the 2-uniform word 12312434 (in this word every pair of letters alternate, except 1 and 4, and 2 and 4), while the graph to the right, the Petersen graph,

6 Read more

On word-representability of polyomino triangulations

On word-representability of polyomino triangulations

We will consider triangulations of a polyomino. Note that no triangulation is 2-colorable – at least three colors are needed to color properly a triangulation, while four colors is always enough to colour any triangulation since we deal with planar graphs and it is well-known that such graphs are 4-colorable [1]. Not all triangulations of a polyomino are 3-colorable – for example, see Figure 1 for non-3-colorable triangulations (which are straightforward to check to require four colors, and also to be the only such triangulations, up to rotations, of a 3 × 3 grid graph). The main result of this paper is the following theorem.
Show more

11 Read more

A Methodology for Obtaining Concept Graphs from Word Graphs

A Methodology for Obtaining Concept Graphs from Word Graphs

It would be interesting to apply this methodology to word graphs generated with a language model, although this way of generating the graphs would not fit exactly the theoretical model. If a language model is used to generate the graphs, then their lex- ical confusion could be reduced, so better results could be achieved. Other interesting task in which this methodology could help is in performing SLU experiments on a combination of the output of some different ASR engines. All these interesting appli- cations constitute a line of our future work.

5 Read more

Semi-transitive orientations and word-representable graphs

Semi-transitive orientations and word-representable graphs

Related work. The notion of directed word-representable graphs was in- troduced in [13] to obtain asymptotic bounds on the free spectrum of the widely-studied Perkins semigroup, which has played central role in semi- group theory since 1960, particularly as a source of examples and coun- terexamples. In [12], numerous properties of word-representable graphs were derived and several types of word-representable and non-word-representable graphs pinpointed. Some open questions from [12] were resolved recently in [7], including the representability of the Petersen graph.
Show more

14 Read more

Word-representability of triangulations of rectangular polyomino with a single domino tile

Word-representability of triangulations of rectangular polyomino with a single domino tile

be one of the four graphs presented in Figure 5 to the right of the leftmost graph. However, in each of the four cases, we have a vertex labeled by * that would require colour 4 contradicting the fact that v is supposed to be the only vertex coloured by 4. This completes our considerations of eight of subcases in the situation S 1 out of 36. The remaining subcases are to be

14 Read more

Learning Word Representations from Relational Graphs

Learning Word Representations from Relational Graphs

We compare the proposed method against several word representation methods in Table 2. All methods in Table 2 use 200 dimensional vectors to represent a word. A baseline method is created that shows the level of performance we can reach if we represent each word u as a vector of patterns l in which u occurs. First, we create a co-occurrence matrix between words u and patterns l, and use Singular Value De- composition (SVD) to create 200 dimensional projections for the words. Because patterns represent contexts in which words appear in the corpus, this baseline can be seen as a version of the Latent Semantic Analysis (LSA), that has been widely used to represent words and documents in infor- mation retrieval. Moreover, SVD reduces the data sparseness in raw co-occurrences. We create three versions of this base- line denoted by SVD+LEX, SVD+POS, and SVD+DEP corresponding to relational graphs created using respec- tively LEX, POS, and DEP patterns. CBOW (Mikolov et al. 2013b), skip-gram (Mikolov et al. 2013c), and GloVe (Pen-
Show more

7 Read more

Word-representability of face subdivisions of triangular grid graphs

Word-representability of face subdivisions of triangular grid graphs

The triangular tiling graph T ∞ (i.e., the two-dimensional triangular grid) is the Archimedean tiling 3 6 introduced in [13] and [4]. By a triangular grid graph G in this paper we mean a graph obtained from T ∞ as follows. Specify a number of triangles, called cells, in T ∞ . The edges of G are then all the edges surrounding the specified cells, while the vertices of G are the endpoints of the edges (defined by intersecting lines in T ∞ ). We say that the specified cells, along with any other cell whose all edges are from G, belong to G. Any triangular grid graph is 3-colorable, and thus it is word-representable [7]. We consider non-3-colorable graphs obtained from triangular grid graphs by applying the operation of face subdivision which is defined in the sequel.
Show more

17 Read more

Word-representability of triangulations of grid-covered cylinder graphs

Word-representability of triangulations of grid-covered cylinder graphs

Our proof is organized as follows. In Subsection 4.1 we will provide all six minimum non-word-representable graphs that can appear in triangulations of GCCGs with three sectors (see Figure 4.11) and give an explicit proof that one of these graphs is non-word-representable. Then, in Subsection 4.2, we will give an inductive argument showing that avoidance of the six graphs in Figure 4.11 is a sufficient condition for a GCCG with three sectors to be word-representable. Note that the graphs in Figure 4.11 were obtained by an exhaustive computer search on graphs on up to eight vertices. However, our argument in Subsection 4.2 will show that no other non-word-representable induced subgraphs can be found among all triangulations of GCCGs with three sectors.
Show more

19 Read more

SINGLE-VALUED NEUTROSOPHIC LINE GRAPHS

SINGLE-VALUED NEUTROSOPHIC LINE GRAPHS

The concept of fuzzy graphs was initiated by Kaufmann [11], based on Zadeh’s fuzzy relations. Later, another elaborated definition of fuzzy graph with fuzzy vertex and fuzzy edges was introduced by Rosenfeld [18] and obtaining analogs of several graph theoretical concepts such as paths, cycles and connectedness etc, he developed the structure of fuzzy graphs. Some remarks on fuzzy graphs were given by Bhattacharya [7]. Fuzzy line graphs were studied in [12] by Mordeson. Nair and Cheng [13] defined the concept of a fuzzy clique consistent with the definition of fuzzy cycles in fuzzy graphs. Intuitionistic fuzzy graphs with vertex sets and edge sets as IFS were introduced by Akram and Davvaz [1]. Sahoo and Pal [19, 20] introduced some new concepts of intuitionistic fuzzy graphs. Naz et al. [3, 16, 17] put forward many new concepts concerning the extended structures of fuzzy graphs. Kandasamy et al. [22] put forward the notion of neutrosophic graphs. Neutrosophic graphs, particularly SVNGs [2, 4, 8, 9, 14, 15] have attracted significant interest from researchers in recent years. In literature, the study of SVNLGs and SVNCs is still blank. To fill this vacancy, we shall focus on the study of SVNLGs and SVNCs, in this paper.
Show more

12 Read more

THE SPLIT COMPLEMENT LINE DOMINATION IN GRAPHS

THE SPLIT COMPLEMENT LINE DOMINATION IN GRAPHS

[2] O.Ore, Theory of graphs, Amer.Math. Soc.Colloq. Publ., 38, Providence, (1962). [3] T.W.Hayness, S.T.Hedetniemi and P.J.Slater, Fundmentals of Domination in graphs, Marcel,Dekker,Inc, Newyork(1998) [4] E.Sampathkumar, The global domination number of a graph J.Math Phys.Sci.23 (1989) 377-385.

16 Read more

On the Limitations of Unsupervised Bilingual Dictionary Induction

On the Limitations of Unsupervised Bilingual Dictionary Induction

duced using the same algorithms with the same hyper-parameters. We evaluate Con- neau et al. (2018) on pairs of embeddings induced with different hyper-parameters in §4.4. While keeping hyper-parameters fixed is always possible, it is of practical interest to know whether the unsupervised methods work on any set of pre-trained word embeddings. We also investigate the sensitivity of unsuper- vised BDI to the dimensionality of the monolin- gual word embeddings in §4.5. The motivation for this is that dimensionality reduction will alter the geometric shape and remove characteristics of the embedding graphs that are important for alignment; but on the other hand, lower dimensionality intro- duces regularization, which will make the graphs more similar. Finally, in §4.6, we investigate the impact of different types of query test words on performance, including how performance varies across part-of-speech word classes and on shared vocabulary items.
Show more

11 Read more

Old and new generalizations of line graphs

Old and new generalizations of line graphs

first characterization (partition into complete subgraphs) was given by Krausz [19]. Since this is a survey on generalizations of line graphs, we will not describe line graphs and their properties in any detail here. Instead, we refer the interested reader to a somewhat older but still an excellent survey on line graphs and line digraphs by Hemminger and Beineke [18]. A more recent book by Prisner [22] describes many interesting generalizations of line graphs. For general graph theoretic concepts and terminology not defined here, please see [9, 16].
Show more

13 Read more

chap01 bk

chap01 bk

Students discover the relationship between algebraic expressions and verbal expressions. They apply their knowledge of basic operations to expressions that include variables. They use the order of operations to solve open sentence equations and inequalities containing a vari- able. Students learn to recognize and use the properties of identity and equality, and the Dis- tributive, Commutative, and Associative Prop- erties. They use these properties to simplify expressions and evaluate equations. Students use tables and coordinates to draw graphs of

72 Read more

On the Wiener Index of Some Total Graphs

On the Wiener Index of Some Total Graphs

V ∪ , and two vertices are adjacent if and only if they are adjacent or incident in G . It is introduced by Behzad & Chartrand [5]. Several properties of total graphs are investigated in the literature (see [1-4,6,7,15,20]). The total graph H = T ( G ) of G is shown in Figure 1.

9 Read more

Line graphs associated to the maximal graph

Line graphs associated to the maximal graph

The following lemma has been proved in [2] for zero-divisor graphs. Exactly the same proof will work for maximal graph, i.e., for Γ(R). Lemma 3.2. Let R be a finite ring. Then L(Γ(R)) is Eulerian if and only if deg(v) is even for all v ∈ V (Γ(R)) or deg(v ) is odd for all v ∈ V (Γ(R)).

11 Read more

Revisiting the Usability of Graphical Displays: an experimental approach

Revisiting the Usability of Graphical Displays: an experimental approach

Each experiment differed in terms of graph format (bar graphs- Group G, curve and line graphs- Group H, and line graphs - Group I) and level of assistance offered to the user (no assista[r]

9 Read more

Degree equitable line domination in graphs

Degree equitable line domination in graphs

The following Theorem relates the degree equitable line domination and roman. domination number in terms of G[r]

10 Read more

On k-Minimally Nonouterplanarity of Line Graphs

On k-Minimally Nonouterplanarity of Line Graphs

Now introduce a point on any nonboundary line in the plane embedding of G but not on the boundary line because if we introduce a point on the boundary line then one point and a line is additional and inner points remain same. The additional line formed in G is again a nonboundary line and by Lemma 2, it corresponds to an inner point in L(G). Thus L(G) is (n+1)-minimally nonouterplanar. This completes the proof of the theorem.

5 Read more

On the Planarity of  Generalized Line Graphs

On the Planarity of Generalized Line Graphs

In this section, we determine all of those trees having planar 3-line graphs. First, we state a well-known characterization of planar graphs. A graph H is a subdivision of a graph G if H can be obtained from G by inserting vertices of degree 2 into some, all or none of the edges of G. Clearly, a subdivision H of a graph G is planar if and only if G is planar. The graphs K 5 and K 3 , 3 and their subdivisions play a pivotal role in the study of planar graphs.

11 Read more

Show all 10000 documents...