• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.937-941
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• 2023

For each positive integer n, a square congruence graph S(n) is the graph with vertex set H = {1, 2, 3,...., n} and two vertices a, b are adjacent if they are distinct and a² ≡ b² (mod n). In this paper we investigate some structural properties of square congruence graph and we obtain the relationship between clique number, chromatic number and maximum degree of square congruence graph. Also we study square congruence graph with p vertices or 2p vertices for any prime number p.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1095-1104
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• 1996

We enumerate the congruence classes of 2-cell embeddings of a dartboard graph into surfaces with respect to a group consisting of graph automorphisms of a dartboard graph.

• ETRI Journal
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• v.29 no.3
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• pp.381-389
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• 2007

In this paper we propose a graph-theoretic method based on linear congruence for constructing low-density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ${\rho}$)-regular quasi-cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit-error-rate performance with iterative decoding in additive white Gaussian noise channels.

• Journal of KIISE:Software and Applications
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• v.32 no.4
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• pp.290-299
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• 2005

Stealing the source code of a program is a serious problem not only in a moral sense but also in a legal sense. However, it is not clear whether the code of a program is copied from another or not. There was a program similarity checker detecting code-copy by comparing the syntax trees of programs. However this method has a limitation that it cannot detect the code-copy attacks when the attacker modifies the syntax of the program on purpose. We propose a program similarity check by program control graph, which reveals not only syntax information but also control dependancy. Our method can detect the code-copy attacks that do not change control dependancy Moreover, we define what code-copy means and establish the connection between code-copy and similarity of program control graph: we prove that two programs are related by copy congruence if and only if the program control graphs of these programs are equivalent. We implemented our method on a functional programming language, nML. The experimental results show us that the suggested method can detect code similarity that is not detected by the existing method.