• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.203-212
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• 2022

A simple graph is called semi-symmetric if it is regular and edge transitive but not vertex transitive. In this paper we prove that there is no connected cubic semi-symmetric graph of order 12p³ for any prime number p.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.83-93
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• 2017

The Cayley graph ${\Gamma}=Cay(G,S)$ is called normal edge-transitive if $N_A(R(G))$ acts transitively on the set of edges of ${\Gamma}$, where $A=Aut({\Gamma})$ and R(G) is the regular subgroup of A. In this paper, we determine all hexavalent normal edge-transitive Cayley graphs on groups of order pqr, where p > q > r > 2 are prime numbers.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.317-324
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• 2001

A Cayley graph of a finite group G is called normal edge-transitive if its automorphism group has a subgroup which both normalized G and acts transitively on edges. In this paper, we consider Cayley graphs of finite cyclic groups, namely, finite circulant graphs. We characterize the normal edge-transitive circulant graphs and determine the normal edge-transitive circulant graphs of prime power order in terms of lexicographic products.

• 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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.3
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• pp.509-516
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• 2021

The transitive signature scheme is a technique that can be very useful when authenticating edges in a graph that is transitively closed. In other words, when there is an authentication value for an edge (i, j) and an authentication value for an edge (j, k), the authentication value for the edge (i, k) can also be calculated immediately without any separate authentication procedure through a transitive signature. In this paper, we propose the first identity-based transitive signature scheme. Our scheme is based on the lattice problem.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.6
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• pp.3316-3332
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• 2019

In a transitive signature scheme, a signer wants to authenticate edges in a dynamically growing and transitively closed graph. Using transitive signature schemes it is possible to authenticate an edge (i, k), if the signer has already authenticated two edges (i, j) and (j, k). That is, it is possible to make a signature on (i, k) using two signatures on (i, j) and (j, k). We propose the first transitive signature schemes for undirected graphs from lattices. Our first scheme is provably secure in the random oracle model and our second scheme is provably secure in the standard model.

• Journal of KIISE:Software and Applications
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• v.27 no.5
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• pp.551-562
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• 2000

Content-based image retrieval system retrieves an image from a database using visual features. Among approaches to express visual aspects in queries, 'query by sketch' is most convenient and expressive. However, every 'query by sketch' system has the query imperfectness problem. GContent-based image retrieval system retrieves an image from a database using visual features. Among approaches to express visual aspects in queries, 'query by sketch' is most convenient and expressive. However, every 'query by sketch' system has the query imperfectness problem. Generally, the query image produced by a user is different from the intended target image. To overcome this problem, many image retrieval systems use the spatial relationships of the objects, instead of pixel coordinates of the objects. In this paper, a query-converting algorithm for an image retrieval system, which uses the spatial relationship of every two objects as an image feature, is proposed. The proposed algorithm converts the query image into a graph that has the minimum number of edges, by eliminating every transitive edge. Since each edge in the graph represents the spatial relationship of two objects, the elimination of unnecessary edges makes the retrieval process more efficient. Experimental results show that the proposed algorithm leads the smaller number of comparison in searching process as compared with other algorithms that do not guarantee the minimum number of edges.