• Title/Summary/Keyword: graph extension

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A Study on the Constructing the Function using Extension Edge Valued Graph (모서리값 확장 그래프를 사용한 함수구성에 관한연구)

  • Park, Chun-Myoung
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.17 no.4
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    • pp.863-868
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    • 2013
  • In recently years, many digital logic systems based on graph theory are analyzed and synthesized. This paper presented a method of constructing the function using edge valued extension graph which is based on graph theory. The graph is applied to a new data structure. from binary graph which is recently used in constructing the digital logic systems based on the graph theory. We discuss the mathematical background of literal and reed-muller expansion, and we discuss the edge valued extension graph which is the key of this paper. Also, we propose the algorithms which is the function derivation based on the proposed edge valued extension graph. That is the function minimization method of the n-variables m-valued functions and showed that the algorithm had the regularity with module by which the same blocks were made concerning about the schematic property of the proposed algorithm.

NONDEGENERATE AFFINE HOMOGENEOUS DOMAIN OVER A GRAPH

  • Choi, Yun-Cherl
    • Journal of the Korean Mathematical Society
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    • v.43 no.6
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    • pp.1301-1324
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    • 2006
  • The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

AN EXTENSION OF ANNIHILATING-IDEAL GRAPH OF COMMUTATIVE RINGS

  • Kerahroodi, Mahtab Koohi;Nabaei, Fatemeh
    • Communications of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.1045-1056
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    • 2020
  • Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R, $^{\bar{\mathbb{AG}}}$(R), is the graph whose vertices are nonzero annihilating ideals of R and two distinct vertices I and J are adjacent if and only if there exist n, m ∈ ℕ such that InJm = (0) with In, Jm ≠ (0). First, we differentiate when 𝔸𝔾(R) and $^{\bar{\mathbb{AG}}}$(R) coincide. Then, we have characterized the diameter and the girth of $^{\bar{\mathbb{AG}}}$(R) when R is a finite direct products of rings. Moreover, we show that $^{\bar{\mathbb{AG}}}$(R) contains a cycle, if $^{\bar{\mathbb{AG}}}$(R) ≠ 𝔸𝔾(R).

AN iP2 EXTENDED STAR GRAPH AND ITS HARMONIOUS CHROMATIC NUMBER

  • P. MANSOOR;A. SADIQUALI
    • Journal of applied mathematics & informatics
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    • v.41 no.6
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    • pp.1193-1207
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    • 2023
  • In this paper, we introduce an iP2 extension of a star graph Sn for n ≥ 2 and 1 ≤ i ≤ n - 1. Certain general properties satisfied by order, size, domination (or Roman) numbers γ (or γR) of an iP2 extended star graph are studied. Finally, we study how the parameters such as chromatic number and harmonious chromatic number are affected when an iP2 extension process acts on the star graphs.

INFORMATION SEARCH BASED ON CONCEPT GRAPH IN WEB

  • Lee, Mal-Rey;Kim, Sang-Geun
    • Journal of applied mathematics & informatics
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    • v.10 no.1_2
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    • pp.333-351
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    • 2002
  • This paper introduces a search method based on conceptual graph. A hyperlink information is essential to construct conceptual graph in web. The information is very useful as it provides summary and further linkage to construct conceptual graph that has been provided by human. It also has a property which shows review, relation, hierarchy, generality, and visibility. Using this property, we extracted the keywords of web documents and made up of the conceptual graph among the keywords sampled from web pages. This paper extracts the keywords of web pages using anchor text one out of hyperlink information and makes hyperlink of web pages abstract as the link relation between keywords of each web page. 1 suggest this useful search method providing querying word extension or domain knowledge by conceptual graph of keywords. Domain knowledge was conceptualized knowledged as the conceptual graph. Then it is not listing web documents which is the defect of previous search system. And it gives the index of concept associating with querying word.

BINDING NUMBERS AND FRACTIONAL (g, f, n)-CRITICAL GRAPHS

  • ZHOU, SIZHONG;SUN, ZHIREN
    • Journal of applied mathematics & informatics
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    • v.34 no.5_6
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    • pp.435-441
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    • 2016
  • Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)-factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811-815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.

SEMISYMMETRIC CUBIC GRAPHS OF ORDER 34p3

  • Darafsheh, Mohammad Reza;Shahsavaran, Mohsen
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.739-750
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    • 2020
  • A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let p be a prime. Folkman proved [J. Folkman, Regular line-symmetric graphs, Journal of Combinatorial Theory 3 (1967), no. 3, 215-232] that no semisymmetric graph of order 2p or 2p2 exists. In this paper an extension of his result in the case of cubic graphs of order 34p3, p ≠ 17, is obtained.

An efficient approach of avoiding extensions of duplicated graph patterns in cyclic graph mining (순환 그래프 마이닝에서 중복된 그래프 패턴의 확장을 피하는 효율적인 기법)

  • No, Young-Sang;Yun, Un-Il;Pyun, Gwang-Bum;Ryang, Heung-Mo;Lee, Gang-In;Ryu, Keun-Ho;Lee, Kyung-Min
    • Journal of the Korea Society of Computer and Information
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    • v.16 no.12
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    • pp.33-41
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    • 2011
  • From Complicated graph structures, duplicated operations can be executed and the operations give low efficiency. In this paper, we propose an efficient graph mining algorithm of minimizing the extension of duplicated graph patterns in which the priorities of cyclic edges are considered. In our approach, the cyclic edges with lower priorities are first extended and so duplicated extensions can be reduced. For performance test, we implement our algorithm and compare our algorithm with a state of the art, Gaston algorithm. Finally, We show that ours outperforms Gaston algorithm.

Improved approach of calculating the same shape in graph mining (그래프 마이닝에서 그래프 동형판단연산의 향상기법)

  • No, Young-Sang;Yun, Un-Il;Kim, Myung-Jun
    • Journal of the Korea Society of Computer and Information
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    • v.14 no.10
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    • pp.251-258
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    • 2009
  • Data mining is a method that extract useful knowledges from huge size of data. Recently, a focussing research part of data mining is to find interesting patterns in graph databases. More efficient methods have been proposed in graph mining. However, graph analysis methods are in NP-hard problem. Graph pattern mining based on pattern growth method is to find complete set of patterns satisfying certain property through extending graph pattern edge by edge with avoiding generation of duplicated patterns. This paper suggests an efficient approach of reducing computing time of pattern growth method through pattern growth's property that similar patterns cause similar tasks. we suggest pruning methods which reduce search space. Based on extensive performance study, we discuss the results and the future works.

Comparison of Objective Functions for Feed-forward Neural Network Classifiers Using Receiver Operating Characteristics Graph

  • Oh, Sang-Hoon;Wakuya, Hiroshi
    • International Journal of Contents
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    • v.10 no.1
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    • pp.23-28
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    • 2014
  • When developing a classifier using various objective functions, it is important to compare the performances of the classifiers. Although there are statistical analyses of objective functions for classifiers, simulation results can provide us with direct comparison results and in this case, a comparison criterion is considerably critical. A Receiver Operating Characteristics (ROC) graph is a simulation technique for comparing classifiers and selecting a better one based on a performance. In this paper, we adopt the ROC graph to compare classifiers trained by mean-squared error, cross-entropy error, classification figure of merit, and the n-th order extension of cross-entropy error functions. After the training of feed-forward neural networks using the CEDAR database, the ROC graphs are plotted to help us identify which objective function is better.