• 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.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.7-14
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• 2001

Let G be a connected graph. A pebbling move on a graph G is taking two pebbles off one vertex and placing one of them on an adjacent vertex. The pebbling number of a connected graph G, f(G), is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the lexicographic products of some graphs are computed.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.685-695
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• 2022

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) ≥ max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.

• The Journal of the Korea Contents Association
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• v.11 no.5
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• pp.67-74
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• 2011

Collaborative recommendation is one of the most widely used methods of automated product recommendation in e-Commerce. For analyzing the customer's preference, traditional explicit ratings are less desirable than implicit ratings because it may impose an additional burden to the customers of e-commerce companies which deals with a number of products. Cardinal scales generally used for representing the preference intensity also ineffective owing to its increasing estimation errors. In this paper, we propose a new way of constructing the ordinal scale-based customer profile for collaborative recommendation. A Web usage mining technique and lexicographic consensus are employed. An experiment shows that the proposed method performs better than existing CF methodologies.