• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.83-93
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• 2017

The Cayley graph ${\Gamma}=Cay(G,S)$ is called normal edge-transitive if $N_A(R(G))$ acts transitively on the set of edges of ${\Gamma}$, where $A=Aut({\Gamma})$ and R(G) is the regular subgroup of A. In this paper, we determine all hexavalent normal edge-transitive Cayley graphs on groups of order pqr, where p > q > r > 2 are prime numbers.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1111-1121
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• 2012

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify tetravalent symmetric graphs of order $9p$ for each prime $p$.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.837-851
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• 2014

We consider ${\omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${\omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${\omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.257-268
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• 2007

An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertex $v_i$ in an oriented graph D is $a_{v_i}\;(or\;simply\;a_i)=n-1+d_{v_i}^+-d_{v_i}^-,\;where\; d_{v_i}^+\;and\;d_{v_i}^-$ are the outdegree and indegree, respectively, of $v_i$ and n is the number of vertices in D. In this paper, we give a new proof of Avery's theorem and obtain some stronger inequalities for scores in oriented graphs. We also characterize strongly transitive oriented graphs.

• 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.

• The Journal of Korean Institute of Information Technology
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• v.16 no.12
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• pp.109-114
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• 2018

Collaborative filtering has been widely utilized in recommender systems as typical algorithm for outstanding performance. Since it depends on item rating history structurally, The more sparse rating matrix is, the lower its recommendation accuracy is, and sometimes it is totally useless. Variety of hybrid approaches have tried to combine collaborative filtering and content-based method for improving the sparsity issue in rating matrix. In this study, a new method is suggested for the same purpose, but with different perspective, it deals with no-match situation in person-person similarity evaluation. This method is called the transitive similarity model because it is based on relation graph of people, and it compares recommendation accuracy by applying to Movielens open dataset.

• Journal of Aerospace System Engineering
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• v.18 no.2
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• pp.1-11
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• 2024

This paper applies a relative impact angle control guidance law to a communication-based multi-missile network system with uncertainties and disturbances. The multi-missile network system is represented as a transitive reduction directed acyclic graph. Furthermore, this paper introduces both centralized and decentralized guidance laws based on the graph's structure. The relationship between these guidance laws is analyzed by comparing them based on the communication structure and the presence of system noise. To analyze the effects of decentralized optimal cooperative guidance law, this paper assumes uncertainty in missile dynamics and predicted impact point information for the relative impact angle control mission. Monte Carlo simulations are conducted for various mission environments to analyze the impact of communication and its structure on the system.