• Title, Summary, Keyword: cubic graph

### CLIQUE-TRANSVERSAL SETS IN LINE GRAPHS OF CUBIC GRAPHS AND TRIANGLE-FREE GRAPHS

• KANG, LIYING;SHAN, ERFANG
• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1423-1431
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• 2015
• A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number is the minimum cardinality of a clique-transversal set in G. For every cubic graph with at most two bridges, we first show that it has a perfect matching which contains exactly one edge of each triangle of it; by the result, we determine the exact value of the clique-transversal number of line graph of it. Also, we present a sharp upper bound on the clique-transversal number of line graph of a cubic graph. Furthermore, we prove that the clique-transversal number of line graph of a triangle-free graph is at most the chromatic number of complement of the triangle-free graph.

### 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.

### CUBIC SYMMETRIC GRAPHS OF ORDER 10p3

• Ghasemi, Mohsen
• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.241-257
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• 2013
• An automorphism group of a graph is said to be $s$-regular if it acts regularly on the set of $s$-arcs in the graph. A graph is $s$-regular if its full automorphism group is $s$-regular. In the present paper, all $s$-regular cubic graphs of order $10p^3$ are classified for each $s{\geq}1$ and each prime $p$.

### CUBIC s-REGULAR GRAPHS OF ORDER 12p, 36p, 44p, 52p, 66p, 68p AND 76p

• Oh, Ju-Mok
• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.651-659
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• 2013
• A graph is $s$-regular if its automorphism group acts regularly on the set of its $s$-arcs. In this paper, the cubic $s$-regular graphs of order 12p, 36p, 44p, 52p, 66p, 68p and 76p are classified for each $s{\geq}1$ and each prime $p$. The number of cubic $s$-regular graphs of order 12p, 36p, 44p, 52p, 66p, 68p and 76p is 4, 3, 7, 8, 1, 4 and 1, respectively. As a partial result, we determine all cubic $s$-regular graphs of order 70p except for $p$ = 31, 41.

### Mathcad program as a useful tool for the teaching and studying the sport biomechanics (운동역학의 교육과 연구용 도구로서 Mathcad의 유용성)

• Sung, Rak-Joon
• Korean Journal of Sport Biomechanics
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• v.14 no.3
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• pp.301-311
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• 2004
• The purpose of this study was to verify the usefulness of the Mathcad program as a tool for the studying and teaching the sport biomechanics. A projectile motion was analyzed because it is the one of the most popular motion in sports activities. A 3 dimensional CG data for the high jump bar clear phase was used to calculate the initial velocity vector of the CG. Linear regression function and other functions such as cubic spline and derivative of Mathcad were used to calculate this vector. Finally, the approach angle to the bar and peak jump height was calculated. Programming in Mathcad was relatively easy compare to traditional computer language such as Fortran and C, because of the unique documentation method of Mathcad. Additionally the 2 and 3 dimensional graph function was very easy and useful to describe the mechanical data. If the use of Mathcad program is more popular in the field of sport biomechanics, it could greatly contribute to overcome the limit of research caused by the lack of proper programming ability.

### ON GRAPHS WITH EQUAL CHROMATIC TRANSVERSAL DOMINATION AND CONNECTED DOMINATION NUMBERS

• Ayyaswamy, Singaraj Kulandaiswamy;Natarajan, Chidambaram;Venkatakrishnan, Yanamandram Balasubramanian
• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.843-849
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• 2012
• Let G = (V, E) be a graph with chromatic number ${\chi}(G)$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every ${\chi}$-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ${\gamma}_{ct}$(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.

### The Fault Tolerance of Interconnection Network HCN(n, n) and Embedding between HCN(n, n) and HFN(n, n) (상호연결망 HCN(n, n)의 고장허용도 및 HCN(n, n)과 HFN(n, n) 사이의 임베딩)

• Lee, Hyeong-Ok;Kim, Jong-Seok
• The KIPS Transactions:PartA
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• v.9A no.3
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• pp.333-340
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• 2002
• Embedding is a mapping an interconnection network G to another interconnection network H. If a network G can be embedded to another network H, algorithms developed on G can be simulated on H. In this paper, we first propose a method to embed between Hierarchical Cubic Network HCN(n, n) and Hierarchical Folded-hypercube Network HFN(n, n). HCN(n, n) and HFN(n, n) are graph topologies having desirable properties of hypercube while improving the network cost, defined as degree${\times}$diameter, of Hypercube. We prove that HCN(n, n) can be embedded into HFN(n, n) with dilation 3 and congestion 2, and the average dilation is less than 2. HFN(n, n) can be embedded into HCN(n, n) with dilation 0 (n), but the average dilation is less than 2. Finally, we analyze the fault tolerance of HCN(n, n) and prove that HCN(n, n) is maximally fault tolerant.

### The Influence of Instrumentalization of Computer Algebra System(CAS) on the Sequence of Mathematics Curriculum in the Optimization Problem Solving Activities of CAS (최적화 문제해결 활동에서 "CAS의 도구화"가 교육과정 내용제시 순서에 미치는 영향)

• Han, Se-Ho
• Journal of Educational Research in Mathematics
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• v.20 no.2
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• pp.185-202
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• 2010
• This study was designed to investigate the possibility that the optimization problem solving activities based on the instrumented CAS can have an influence on the sequence of mathematics curriculum in secondary mathematics education. Some optimization problem solving activities based on CAS were constructed and executed to eleventh grade(the penultimate year of Korean high school) 7 students for nine class hours. They have experienced using CAS in mathematics class for three months, but never learned calculus. The data which consists of classroom observations(audio and video taped) and post-unit interviews with students were analyzed. In the analysis, with CAS, students can highly deal with the applied optimization problems made up of calculus, cubic equation, solution of radical equation, and graph analysis which never learned. This result shows CAS may have an influence on the sequence of mathematics curriculum in secondary mathematics education.