• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.287-293
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• 2023

In this paper, the Augmented graph Es(τ) of the inverse graph Gs(τ) of a cyclic group (τ,◦) was studied. The Augmented inverse graph was constructed by applying the method of Mycielski's construction. The dimension of Augmented inverse graph and different properties of the graph were investigated. Later the chromatic number of Augmented inverse graph was discussed and the relation between the maximum degree of the graph and the chromatic number was established. In the Mycielski's construction, the properties of the key node 'u' in Es (τ) were established based on cardinality of the cyclic group (τ,◦) and also proved that the Augmented inverse graph Es(τ) was a triangle free graph.

• 한국컴퓨터정보학회논문지
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• 제24권10호
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• pp.57-64
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• 2019

이 논문에서는 인터벌 그래프 컬러링 역문제 중 다항시간 안에 풀이 가능한 경우에 대해 연구한다. 인터벌 그래프의 컬러링 역문제는 주어진 인터벌 그래프를 K개의 서로 다른 색깔로 색칠할 수 없는 경우를 가정하며, 다음과 같이 정의된다. 주어진 인터벌 그래프가 K개의 색깔을 이용해서 모두 칠해질 수 있도록 인터벌 그래프와 연관되어 있는 인터벌 시스템을 최소한으로 수정하는 문제이다. 인터벌 시스템에서 두 인터벌이 부분적으로라도 서로 겹쳐있는 구간이 있을 경우 두 인터벌에 해당하는 노드들이 엣지로 연결되어 있음을 의미하고, 따라서 이 경우에는 해당 노드들을 같은 색깔을 이용해 칠할 수 없다. 따라서 겹쳐져 있는 인터벌들을 이동시켜 해당 그래프의 chromatic number를 바꿀 수 있다. 본 논문에서는 인터벌의 길이가 모두 1 또는 2이며, 인터벌의 이동이 본래 위치 대비 오른쪽으로만 가능하다는 제한이 있는 경우에 대해 집중 탐구한다. 이 문제를 해결하는 다항시간 알고리즘으로 sorting과 선입선출 방식을 사용하는 2단계 알고리즘을 제안한다.

• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.467-475
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• 2020

Let G be a chemical graph with vertex set {v₁, v₁, …, v_n} and degree sequence d(G) = (deg_G(v₁), deg_G(v₂), …, deg_G(v_n)). The inverse degree, R(G) of G is defined as $R(G)={\sum{_{i=1}^{n}}}\;{\frac{1}{deg_G(v_i)}}$. The cyclomatic number of G is defined as γ = m - n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.221-225
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• 2016

For a connected graph G = (V, E), its inverse degree is defined as $\sum_{{\upsilon}{\in}{V}}^{}\frac{1}{d(\upsilon)}$. Using an upper bound for the inverse degree of a graph obtained by Cioabă in [4], we in this note present sufficient conditions for some Hamiltonian properties and k-connectivity of a graph.

• 제어로봇시스템학회논문지
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• 제20권5호
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• pp.526-532
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• 2014

In this paper, we present and analyze a LQ (Linear Quadratic) inverse optimal state-consensus protocol for continuous-time multi-agent systems with undirected graph topology. By Lyapunov analysis of the state-consensus error dynamics, we show the sufficient conditions on the algebraic connectivity of the graph to guarantee LQ inverse optimality and closed-loop stability. A more relaxed stability condition is also provided in terms of the algebraic connectivity. Finally, a formation control protocol for multiple mobile robots is proposed based on the target LQ inverse optimal consensus protocol, and the simulation results are provided to verify the performance of the proposed LQ inverse formation control method.

• 한국경영과학회지
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• 제39권2호
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• pp.131-140
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• 2014

Customer networks go through constant changes. They may expand or shrink once they are formed. In dynamic environments, it is a critical corporate challenge to identify and manage influential customer groups in a cost effective way. In this context, we apply inverse optimization theory to suggest an efficient method to manage customer networks. In this paper, we assume that there exists a subset of nodes that might have a large effect on the network and that the network can be modified via some strategic actions. Rather than making efforts to find influential nodes whenever the network changes, we focus on a subset of selective nodes and perturb as little as possible the interaction between nodes in order to make the selected nodes influential in the given network. We define the following problem based on the inverse optimization. Given a graph and a prescribed node subset, the objective is to modify the structure of the given graph so that the fixed subset of nodes becomes a minimum dominating set in the modified graph and the cost for modification is minimum under a fixed norm. We call this problem the inverse dominating set problem and investigate its computational complexity.

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.561-570
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• 2005

Weak Crossed Product Algebras correspond to certain graphs called lower subtractive graphs. The properties of such algebras can be obtained by studying this kind of graphs ([4], [5]). In [1], the author showed that a weak crossed product is Frobenius and its restricted subalgebra is symmetric if and only if its associated graph has a unique maximal vertex. A special construction of these graphs came naturally and was known as standard lower subtractive graph. It was a deep question that when such a special graph possesses unique maximal vertex? This work is to answer the question partially and to give a particular characterization for such graphs at which the corresponding algebras are isomorphic. A graph that follows the mentioned characterization is called flexible. Flexibility is to some extend a generalization of the so-called Coxeter groups and its weak Bruhat ordering.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.193-203
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• 2007

In this paper we consider the inverse minimum flow (ImF) problem, where lower and upper bounds for the flow must be changed as little as possible so that a given feasible flow becomes a minimum flow. A linear time and space method to decide if the problem has solution is presented. Strongly and weakly polynomial algorithms for solving the ImF problem are proposed. Some particular cases are studied and a numerical example is given.

• 제어로봇시스템학회논문지
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• 제21권5호
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• pp.434-441
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• 2015

In this paper, we propose an inverse optimal distributed protocol for the formation and velocity consensus of nonholonomic mobile robots. The communication among mobile robots is described by a simple undirected graph, and the mobile robots' kinematics are considered. The group of mobile robots driven by the proposed protocols asymptotically achieves the desired formation and group velocity in an inverse optimal fashion. The design of the protocols is based on dynamic feedback linearization and the proposed linear quadratic (LQ) inverse optimal second-order consensus protocol. A numerical simulation is given to verify the effectiveness of the proposed scheme.

• 대한수학회보
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• 제54권2호
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• pp.507-519
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• 2017

We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of ${\beta}$-Laplacian for some positive real number ${\beta}$. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.