• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.771-784
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• 1998

In this paper we propose an algorithm for generating minimal cutsets of undirected graphs. The algorithm is based on a blocking mechanism for generating every minimal cutest ex-actly once. The algorithm has an advantage of not requiring any preliminary steps to find minimal cutsets. The algorithm generates minimal cutsets at O(e.n) {where e,n = number of (edges, vertices) in the graph} computational effort per cutset. Formal proofs of the algorithm are presented.

• Journal of the Korea Society of Computer and Information
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• v.19 no.7
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• pp.103-111
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• 2014

This paper proposes a modified algorithm that improves on Dijkstra's algorithm by applying it to purely two-way traffic paths, given that a road where bi-directional traffic is made possible shall be considered as an undirected graph. Dijkstra's algorithm is the most generally utilized form of shortest-path search mechanism in GPS navigation system. However, it requires a large amount of memory for execution for it selects the shortest path by calculating distance between the starting node and every other node in a given directed graph. Dijkstra's algorithm, therefore, may occasionally fail to provide real-time information on the shortest path. To rectify the aforementioned shortcomings of Dijkstra's algorithm, the proposed algorithm creates conditions favorable to the undirected graph. It firstly selects the shortest path from all path vertices except for the starting and destination vertices. It later chooses all vertex-outgoing edges that coincide with the shortest path setting edges so as to simultaneously explore various vertices. When tested on 9 different undirected graphs, the proposed algorithm has not only successfully found the shortest path in all, but did so by reducing the time by 60% and requiring less memory.

• Journal of Information Processing Systems
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• v.15 no.6
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• pp.1365-1377
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• 2019

Summarizing the differences in Chinese-Vietnamese bilingual news plays an important supporting role in the comparative analysis of news views between China and Vietnam. Aiming at cross-language problems in the analysis of the differences between Chinese and Vietnamese bilingual news, we propose a new method of summarizing the differences based on an undirected graph model. The method extracts elements to represent the sentences, and builds a bridge between different languages based on Wikipedia's multilingual concept description page. Firstly, we calculate the similarity between Chinese and Vietnamese news sentences, and filter the bilingual sentences accordingly. Then we use the filtered sentences as nodes and the similarity grade as the weight of the edge to construct an undirected graph model. Finally, combining the random walk algorithm, the weight of the node is calculated according to the weight of the edge, and sentences with highest weight can be extracted as the difference summary. The experiment results show that our proposed approach achieved the highest score of 0.1837 on the annotated test set, which outperforms the state-of-the-art summarization models.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.85-98
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• 2012

Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(${\Gamma}_I(R)$). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y ${\in}$ R, the vertices x and y are adjacent if and only if x + y ${\in}$ S(I). The total graph of a commutative ring, that denoted by T(${\Gamma}(R)$), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y ${\in}$ Z(R) which is due to Anderson and Badawi [2]. In the case I = {0}, $T({\Gamma}_I(R))=T({\Gamma}(R))$; this is an important result on the definition.

• Journal of the Korea Society of Computer and Information
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• v.12 no.2 s.46
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• pp.181-188
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• 2007

Undirected Rural Postman Problem(URPP) is a problem that finds a shortest tour traversing the given arcs at least once in a given network. The URPP is one of the basic network problems used in solving the various real-world problems. And it is known as NP-Complete. URPP is an arc-oriented problem that the direction of a tour in an arc has to be considered. Hence, In URPP, it is difficult to use the algorithm for Traveling Salesman Problem (TSP), which is a node-oriented problem, directly. This paper proposes the decoding algorithm using graph transformation in the genetic algorithm for URPP. That is, you can find the entire tour traversing without considering the direction of arcs by transforming the arc-oriented graph into the node-oriented graph. This paper compares the performances of the proposed algorithm with an existing algorithm. In the simulation results, the proposed algorithm obtained better than the existing algorithm

• Honam Mathematical Journal
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• v.40 no.1
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• pp.75-82
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• 2018

Let P be a commutator poset with Z(P) its set of zero-divisors. The annihilator graph of P, denoted by AG(P), is the (undirected) graph with all elements of $Z(P){\setminus}\{0\}$ as vertices, and distinct vertices x, y are adjacent if and only if $ann(xy)\;{\neq}\;(x)\;{\cup}\;ann(y)$. In this paper, we study basic properties of AG(P).

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1323-1336
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• 2015

Let S be a semigroup with 0 and R be a ring with 1. We extend the definition of the zero-divisor graphs of commutative semigroups to not necessarily commutative semigroups. We define an annihilating-ideal graph of a ring as a special type of zero-divisor graph of a semigroup. We introduce two ways to define the zero-divisor graphs of semigroups. The first definition gives a directed graph ${\Gamma}$(S), and the other definition yields an undirected graph ${\overline{\Gamma}}$(S). It is shown that ${\Gamma}$(S) is not necessarily connected, but ${\overline{\Gamma}}$(S) is always connected and diam$({\overline{\Gamma}}(S)){\leq}3$. For a ring R define a directed graph ${\mathbb{APOG}}(R)$ to be equal to ${\Gamma}({\mathbb{IPO}}(R))$, where ${\mathbb{IPO}}(R)$ is a semigroup consisting of all products of two one-sided ideals of R, and define an undirected graph ${\overline{\mathbb{APOG}}}(R)$ to be equal to ${\overline{\Gamma}}({\mathbb{IPO}}(R))$. We show that R is an Artinian (resp., Noetherian) ring if and only if ${\mathbb{APOG}}(R)$ has DCC (resp., ACC) on some special subset of its vertices. Also, it is shown that ${\overline{\mathbb{APOG}}}(R)$ is a complete graph if and only if either $(D(R))^2=0,R$ is a direct product of two division rings, or R is a local ring with maximal ideal m such that ${\mathbb{IPO}}(R)=\{0,m,m^2,R\}$. Finally, we investigate the diameter and the girth of square matrix rings over commutative rings $M_{n{\times}n}(R)$ where $n{\geq} 2$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.6
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• pp.3316-3332
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• 2019

In a transitive signature scheme, a signer wants to authenticate edges in a dynamically growing and transitively closed graph. Using transitive signature schemes it is possible to authenticate an edge (i, k), if the signer has already authenticated two edges (i, j) and (j, k). That is, it is possible to make a signature on (i, k) using two signatures on (i, j) and (j, k). We propose the first transitive signature schemes for undirected graphs from lattices. Our first scheme is provably secure in the random oracle model and our second scheme is provably secure in the standard model.

• The Mathematical Education
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• v.13 no.2
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• pp.6-10
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• 1974

We consider 'ordinary' graphs: that is, finite undirected graphs with no loops or multiple edges. An intersection representation of a graph G is a function r from V(G), the set of vertices of G, into a family of sets S such that distinct points $\chi$$_{\alpha}$ and $\chi$$_{\beta}$/ of V(G) are. neighbors in G precisely when ${\gamma}$($\chi$$_{\alpha}$)∩${\gamma}$($\chi$$_{\beta}$/)$\neq$ø, A graph G is a rigid circuit grouph if every cycle in G has at least one triangular chord in G. In this paper we consider the main theorem; A graph G has an intersection representation by arcs on an acyclic graph if and only if is a normal rigid circuit graph.uit graph.d circuit graph.uit graph.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.65-75
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• 2007

A graph G is self-complementary (sc) if it is isomorphic to its complement. G is perfect if for all induced subgraphs H of G, the chromatic number of H (denoted ${\chi}$(H)) equals the number of vertices in the largest clique in H (denoted ${\omega}$(H)). An sc graph which is also perfect is known as sc perfect graph. A comparability graph is an undirected graph if it can be oriented into transitive directed graph. An sc comparability (scc) is clearly a subclass of sc perfect graph. In this paper we show that no two non-isomorphic scc graphs with n vertices each, (n<13) have same spectrum, and that the smallest positive integer for which there exists hyper-energetic scc graph is 13.