• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.65-72
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• 1998

Many optimization problems like domination and Steiner tree are NP-complete on chordal graphs but can be solved in polyno-mial time on doubly chordal graphs. Investigating properties of dou-bly chordal graphs probably help to design efficient algorithms for the graphs. We present some characterizations of dobly chordal graphs which are based on clique matrices and neighborhood matrics also men-tioned how a doubly perfect elimination ordering of a doubly chordal graph can be computed from the results.

• 전기의세계
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• v.19 no.5
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• pp.1-7
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• 1970

Starting from the review of signal flow graphs and flow graphs, this paper gives an example of sampled-data systems for Sedlar & Bekey's formulation. In this purpose it discussed the difference between Mason's signal-flow graphs and Coates flow graphs for drawing th flow graph of a linear system, and then a new flow-graph symbol introduced in order to distinguish between continuous and discrete systems. Thus, the paper is analysed and compared with a sampled-data systems between conventional methods and new method of signal flow graphs.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.301-307
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• 2017

In this paper, we solve the following four graph equations $L^k(G)=H{\oplus}J$; $M(G)=H{\oplus}J$; ${\bar{L^k(G)}}=H{\oplus}J$ and ${\bar{M(G)}}=H{\oplus}J$, where J is $nK_2$ for $n{\geq}1$. Here, the equality symbol = means the isomorphism between the corresponding graphs. In particular, we shall obtain all pairs of graphs (G, H), which satisfy the above mentioned equations, upto isomorphism.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.661-669
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• 2021

For a simple, undirected graph G = (V, E), a perfect Roman dominating function (PRDF) f : V → {0, 1, 2} has the property that, every vertex u with f(u) = 0 is adjacent to exactly one vertex v for which f(v) = 2. The weight of a PRDF is the sum f(V) = ∑_v∈V f(v). The minimum weight of a PRDF is called the perfect Roman domination number, denoted by γ_R^P(G). Given a graph G and a positive integer k, the PRDF problem is to check whether G has a perfect Roman dominating function of weight at most k. In this paper, we first investigate the complexity of PRDF problem for some subclasses of bipartite graphs namely, star convex bipartite graphs and comb convex bipartite graphs. Then we show that PRDF problem is linear time solvable for bounded tree-width graphs, chain graphs and threshold graphs, a subclass of split graphs.

• Journal of Information Technology Applications and Management
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• v.22 no.3
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• pp.65-81
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• 2015

This study reports a preliminary finding of the types and numbers of graphs being presented in the annual reports of about thirty top listed companies trading publicly in the stock markets of three countries-Thailand (SET), Malaysia (BM), and Singapore (SGX)-that were chosen based on their inclusion in the ASEAN Stars Index under the ASEAN Trading Link project. A total of 6,753 graphs from nineteen sectors were extracted and examined. Banking, real estate, and telecommunications are ranked the three most condense sectors, accounting for 50.2% of the total number of graphs observed. The three most used graphs are the Conservative Bar, Donut graph and Stack Bar. Less than one percent of Infographic type graphs were used. The five most depicted graphed variables are Asset, Revenue, Net profit, Liability, and Dividend. Using rudimentary framework to detect distorted or misleading statistical graphs, the study found 60.6% of the graphs distorted across the three markets, SET, BM, and SGX. BM ranked first in percentages of graphs being distortedly presented (73%). The other two markets, SET and SGX, have about the same proportions, 53.88% and 53.03%, respectively. Likewise, the proportions of Well-designed versus Inappropriate-designed graphs of the latter two markets are a little over one time (SET = 1 : 1.17; SGX = 1 : 1.13), whereas the proportion is almost triple for the BM market (BM = 1 : 2.70). In addition, the trend of distorted graphs found is slightly increasing as the longevity of the ASEAN Stars Index increases. One possible explanation for the relatively equal proportion of inappropriate graphs found is that SET is the smallest market and SGX, though the largest, is the most regulated market. BM, on the other hand, may want to present their financial data in the most attractive manner to prospective investors, thus, regulatory constraints and governance structure are still lenient.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.21-38
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• 2006

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs restricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamiltonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be generated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underlying graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.

• Education of Primary School Mathematics
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• v.23 no.4
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• pp.157-173
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• 2020

Although there are various form of statistical graphs in the real world, the statistical graphs in elementary mathematics textbooks are very formalized by the pedagogical constraints. In this study, I examine the frames of statistical graphs and their educational importance, and analyze the frames in Korean, Australian, and MiC textbooks. As a result, the frames of statistical graphs in elementary mathematics textbooks (1) draws students' attention to the components of the graphs, (2) plays a supplementary role in students' drawing graphs by hands, and (3) helps to apply school mathematics to statistical problem solving in real life. The frames of statistical graphs in Korean textbooks is the form of tables focusing on (1) and (2), but these of MiC textbooks has various forms focusing on (3). On the other hand, Austalian textbooks introduced the table-form frames of statistical graphs at the lower graders, but gradually changed to the axis-form frames as the grade level increased. Based on this, a recommendation was drawn on how to deal with the frames of statistical graphs in elementary mathematics textbooks.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.1
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• pp.57-61
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• 1984

This paper deals with the selection of minimal test instruction set for microprocessor data processing test. This test method is based on a function description of the instructions which are obtained from the data given by the user's manual. Selecting procedure is done in 3 steps: 1) a test execution graphs are represented on the instructions which are grouped functionally, 2) the essential graphs, the eliminable graphs, the eliminable graphs, and the eligible graphs are built, 3) optimal test instruction set from the essential graphs and the eligible graphs is defined. In the case of INTEL 8048, 50 test instructions can be selected optimally from 8048 instruction repertories (96 instructions)

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.95-111
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• 2017

Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.847-856
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• 2005

M. Junger, G. Reinelt, and W. R. Pulleyblank asked the following questions ([2]). (1) Is it true that every simple planar 2-edge connected bipartite graph has a 3-partition in which each component consists of the edge set of a simple path? (2) Does every simple planar 2-edge connected graph have a 3-partition in which every component consists of the edge set of simple paths and triangles? The purpose of this paper is to provide a positive answer to the second question for simple outerplanar 2-vertex connected graphs and a positive answer to the first question for simple planar 2-edge connected bipartite graphs one set of whose bipartition has at most 4 vertices.