• KIPS Transactions on Computer and Communication Systems
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• v.4 no.2
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• pp.37-40
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• 2015

In this paper, we present linear, varied and mixed edge labeling methods using 2-edge labeling on binomial trees. As a result of this paper, we can design the variable topologies to enable optimal broadcasting with binomial tree as spanning tree, if we use these edge labels as the jump sequence of a sort of interconnection networks, circulant graph, with maximum connectivity and high reliability.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.6
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• pp.437-450
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• 2009

In this paper, we propose seven edge labeling methods. The methods produce three case of edge labels-sets of Fibonacci numbers {$F_k|k\;{\geq}\;2$}, {$F_{2k}|k\;{\geq}\;1$} and {$F_{3k+2}|k\;{\geq}\;0$}. When a sort of interconnection network, the circulant graph is designed, these edge labels are used for its jump sequence. As a result, the degree is due to the edge labels.

• Proceedings of the Korea Information Processing Society Conference
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• 2013.05a
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• pp.195-197
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• 2013

본 논문에서는 이항트리에서의 선형적 에지번호매김방법과 변형된 에지번호매김방법을 제안한다. 이러한 연구결과는 최대 연결도를 갖는 신뢰성이 높은 상호연결망의 일종인 원형군 그래프(circulant graph)의 점프열(jump sequence)로 에지번호들을 사용하면 이항트리를 스패닝 트리로 갖고 최적방송이 가능한 위상설계를 할 수 있다.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.42 no.1
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• pp.27-34
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• 2005

In this paper, we propose the Q-edge labeling method related to the graph embedding problem in binomial trees. This result is able to design a new reliable interconnection networks with maximum connectivity using Q-edge labels as jump sequence of circulant graph. The circulant graph is a generalization of Harary graph which is a solution of the optimal problem to design a maximum connectivity graph consists of n vertices End e edgies. And this topology has optimal broadcasting because of having binomial trees as spanning tree.

• Proceedings of the IEEK Conference
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• 2004.06a
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• pp.167-170
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• 2004

We present a novel graph labeling problem called S-edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be ${ a_n / a_n = 4 a_{n-l}+l,\;a_{n-1}=0}$. We show that every binomial tree is possible S-edge labeling by giving labeling schems to them. The labelings on the binomial trees are applied to their embedings into interconnection networks.