Character Graph Research Articles

N-Exact character graphs

Let Γ be a finite simple graph. If for some integer Γ is a Kn -free graph whose complement has an odd cycle of length at least then we say that Γ is an n-exact graph. For a finite group G, let denote the character graph built on the set of degrees of the irreducible complex characters of G. In this paper, we prove that the order of an n-exact character graph is at most Also we determine the structure of all finite groups G with extremal n-exact character graph.

Disconnected character graphs and odd dominating sets

Suppose Γ is a finite simple graph. If D is a dominating set of Γ such that each is contained in the set of vertices of an odd cycle of Γ, then we say that D is an odd dominating set for Γ. For a finite group G, let denote the character graph built on the set of degrees of the irreducible complex characters of G. In this paper, we show that the complement of contains an odd dominating set, if and only if is a disconnected graph with non-bipartite complement.

On cut vertices and eigenvalues of character graphs of solvable groups

Given a finite group G, the character graph, denoted by Δ(G), for its irreducible character degrees is a graph with vertex set ρ(G) which is the set of prime numbers that divide the irreducible character degrees of G, and with {p,q} being an edge if there exists a non-linear χ∈Irr(G) whose degree is divisible by pq. In this paper, on one hand, we proceed by discussing the graphical shape of Δ(G) when it has cut vertices or small number of eigenvalues, and on the other hand we give some results on the group structure of G with such Δ(G). Recently, Lewis and Meng proved the character graph of each solvable group has at most one cut vertex. Now, we determine the structure of character graphs of solvable groups with a cut vertex and diameter 3. Furthermore, we study solvable groups whose character graphs have at most two distinct eigenvalues. Moreover, we investigate the solvable groups whose character graphs are regular with three distinct eigenvalues. In addition, we give some lower bounds for the number of edges of Δ(G).

THE CHARACTER GRAPH OF A FINITE GROUP IS PERFECT

AbstractFor a finite group G, let $\Delta (G)$ denote the character graph built on the set of degrees of the irreducible complex characters of G. A perfect graph is a graph $\Gamma $ in which the chromatic number of every induced subgraph $\Delta $ of $\Gamma $ equals the clique number of $\Delta $ . We show that the character graph $\Delta (G)$ of a finite group G is always a perfect graph. We also prove that the chromatic number of the complement of $\Delta (G)$ is at most three.

Dynamic character graph via online face clustering for movie analysis

An effective approach to automated movie content analysis involves building a network (graph) of its characters. Existing work usually builds a static character graph to summarize the content using metadata, scripts or manual annotations. We propose an unsupervised approach to building a dynamic character graph that captures the temporal evolution of character interaction. We refer to this as the character interaction graph (CIG). Our approach has two components: (i) an online face clustering algorithm that discovers the characters in the video stream as they appear, and (ii) simultaneous creation of a CIG using the temporal dynamics of the resulting clusters. We demonstrate the usefulness of the CIG for two movie analysis tasks: narrative structure (acts) segmentation and major character retrieval. Our evaluation on full-length movies containing more than 5000 face tracks shows that the proposed approach achieves superior performance for both the tasks.

Character graphs with diameter three

For a finite group G G , let Δ ( G ) \Delta (G) denote the character graph built on the set of degrees of the irreducible complex characters of G G . In this paper, we show that if the diameter of Δ ( G ) \Delta (G) is equal to three, then the complement of Δ ( G ) \Delta (G) is bipartite. Also in this case, we determine the structure of the character graph Δ ( G ) \Delta (G) .

Regional Bullying Text Recognition Based on Two-Branch Parallel Neural Networks

Traditional features and pipelined algorithms ignore the subspace semantic information and different information complementarity of regional bullying text when describing and recognizing regional bullying text. In order to solve the above problems, combined with features of Chinese, a regional bullying text recognition algorithm called Two-Branch Parallel Neural Network (TB-PNN) is proposed. First, the word vector, sentence vector, pinyin and tone features extracted by the word embedding technique and the character feature extracted by the Character Graph Convolutional Neural (CGCN). Secondly, TB-PNN is constructed by Multi-Head Self-Attention Mechanism (MHSA), Capsule Network (CapsNet) and Independent Recurrent Neural Network (IndRNN). The left branch was MHSA-CapsNet and the right branch was Multi-MHSA-IndRNN. The algorithm assigns weights to the fused features through MHSA, uses the CapsNet of the left branch to mine the key features with high weight and generates vector tags, and uses the IndRNN of the right branch to capture the subspace semantic information of the key features in the text. The left and right branches form complementary information. Finally, SoftMax classifier is used to realize the accurate recognition of regional bullying text. The experimental results show that TB-PNN algorithm can effectively improve the recognition accuracy of regional bullying text.

Joint extraction of entities and relations based on character graph convolutional network and Multi-Head Self-Attention Mechanism

ABSTRACT The traditional method of extracting entities and relations not only disregards the dependency between the two subtasks of entities and relations but also facilitates the cumulative propagation of errors. To solve these problems, a method – called MSBD – of joint extraction of entities and relations based on the Character Graph Convolutional Network (CGCN) and Multi-Head Self-Attention Mechanism (MS) is proposed. First, a new tagging scheme is used to tag the positions of entities and relations in the text. Second, to depict the hierarchical structure information between the entities and the relations in the text and the internal structure information of the entity, the CGCN is designed to obtain the character vector of the text. MS is introduced into the coding framework of Bidirectional Long Short-Term Memory (BiLSTM) to capture the relative position information between two entities in the text and represent the subspace information. The Dense Connected Convolutional Network (Dense Net) is embedded in the decoding framework to enhance the reuse and transmission of key information and achieve joint extraction of entities and relations in the text. The experimental results show that the P, R and F values are significantly improved for extracting entities and relations.

Named-Entity Recognition in Sports Field Based on a Character-Level Graph Convolutional Network

Traditional methods for identifying naming ignore the correlation between named entities and lose hierarchical structural information between the named entities in a given text. Although traditional named-entity methods are effective for conventional datasets that have simple structures, they are not as effective for sports texts. This paper proposes a Chinese sports text named-entity recognition method based on a character graph convolutional neural network (Char GCN) with a self-attention mechanism model. In this method, each Chinese character in the sports text is regarded as a node. The edge between the nodes is constructed using a similar character position and the character feature of the named-entity in the sports text. The internal structural information of the entity is extracted using a character map convolutional neural network. The hierarchical semantic information of the sports text is captured by the self-attention model to enhance the relationship between the named entities and capture the relevance and dependency between the characters. The conditional random fields classification function can accurately identify the named entities in the Chinese sports text. The results conducted on four datasets demonstrate that the proposed method improves the F-Score values significantly to 92.51%, 91.91%, 93.98%, and 95.01%, respectively, in comparison to the traditional naming methods.

Building Character Graphs and Dividing Communities in Chinese Novels Based on Graph Data Extraction: Community Division for Character Emotional Polarity Networks

Chinese authors indirectly portray real social relationships in society by incorporating their own experiences and feelings about politics, economic life, and cultural habits. Social and natural knowledge are mixed and hidden in natural literary language. Therefore, by well defining the type of original text, the pipeline for processing the text and the rules to build the graph, we can extract enough valid and useful information. Based on higher-level information, we can build a literary character graph to promote computers' comprehension of literature. The identification of opposite characters is a challenging topic because the character relationships are intricate and complex. The cryptic expression in literary works can enhance the readability of the plot, but it is obvious that it increases the cost of understanding. Even for human readers different types of characters are difficult to classify and identify, and it usually needs careful reading for several times to get the subtle differences among the characters. Though extracting knowledge from Chinese literature is a complicated and difficult topic, this paper models the graph of polar literary characters and divides polar communities by extracting polar vertices and polar edges based on the concept of literary sentiment polarity. The results show that using a long-sentence window is a good trade-off. The experiments of modern Chinese polar literature show that the accuracy of the community division method for the integrated graph polarity is obviously better than the method based on the co-occurrence network, and it can automatically match the positive and negative communities as well as build the complete graph structure. It clearly reflects the meaning of literary works from the perspective of polarity. This systematic model describes general standard operation steps for the machine to understand complex Chinese literature. The experiments conducted on seven benchmark Chinese novel datasets demonstrate that the method based on emotional polarity shows a significant improvement compared to baseline performance. Though we use Chinese datasets in this paper, the model and methods are important references for literature analysis and graph extraction in other languages.

CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT

For a finite group $G$, let $\unicode[STIX]{x1D6E5}(G)$ denote the character graph built on the set of degrees of the irreducible complex characters of $G$. In this paper, we obtain a necessary and sufficient condition which guarantees that the complement of the character graph $\unicode[STIX]{x1D6E5}(G)$ of a finite group $G$ is a nonbipartite Hamiltonian graph.

K4-free character graphs with seven vertices

For a finite group G, let Δ(G) denote the character graph built on the set of degrees of the irreducible complex characters of G. In this article, we determine the structure of all finite groups G with K4-free character graph Δ(G) having seven vertices. We also obtain a classification of all K4-free graphs with seven vertices which can occur as character graphs of some finite groups.

Coloring of character graphs

ABSTRACTIn this paper, we study the character graph Δ(G) of a finite solvable group G. We prove that sum of the chromatic number of Δ(G) and the matching number of complement graph of Δ(G) is equal to the order of Δ(G). Also, we prove that when Δ(G) is not a block, the chromatic number of Δ(G) is equal to the clique number of Δ(G).

Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles

Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud' in their book “Characters of Finite Groups”, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs (associated with degrees) have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.

Hamiltonian character graphs

In this paper, we obtain a necessary and sufficient condition which guarantees that the character graph of a solvable group is Hamiltonian. In the continuation, we present classes of solvable groups whose character graphs are Hamiltonian.

A Study on the Chinese Character Graph and Expression Methods for an effective communication -The Combination of Chinese Characters and Formation-

A Study on the Chinese Character Graph and Expression Methods for an effective communication -The Combination of Chinese Characters and Formation-

Relative character graphs related to GL(2,q) and its subgroups

Relative character graphs related to GL(2,q) and its subgroups

Relative character graphs: some properties and examples

Let G be a finite group and H be a subgroup of G. T. Gnanaseelan and C. Selvaraj defined a graph Γ(G,H) by using the irreducible characters of G and the restrictions of these characters to H. In this paper we continue the study of the connected components of these graphs. We also study examples of these graphs for some specific groups.

Finite nonsolvable groups whose character graphs have no triangles

In this paper, we show that the alternating group A 5 is the only nonsolvable group whose character graph has no triangles.

Tone-enhanced generalized character posterior probability (GCPP) for Cantonese LVCSR

Tone-enhanced generalized character posterior probability (GCPP), a generalized form of posterior probability at subword (Chinese character) level, is proposed as a rescoring metric for improving Cantonese LVCSR performance. GCPP is computed by tone score along with the corresponding acoustic and language model scores. The tone score is output from a supra-tone model, which characterizes not only the tone contour of a single syllable but also that of adjacent ones and significantly outperforms other conventional tone models. The search network is constructed first by converting the original word graph to a restructured word graph, then a character graph and finally, a character confusion network (CCN). Based upon tone-enhanced GCPP, the character error rate (CER) is minimized or the GCPP product is maximized over a chosen graph. Experimental results show that the tone-enhanced GCPP can improve character error rate by up to 15.1%, relatively.