• Honam Mathematical Journal
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• v.27 no.2
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• pp.183-194
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• 2005

A permutation graph is the graph of inversions in a permutation. Here we determine whether a given labelled graph is a permutation graph or not and when a graph is a permutation graph we find the associated permutation. We also characterize all the 2-regular permutation graphs.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.551-559
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• 2005

A permutation graph over a graph G is a generalization of both a graph bundle and a graph covering over G. In this paper, we characterize the F-permutation graphs over a graph whose chromatic numbers are 2. We determine the chromatic numbers of $C_n$-permutation graphs over a tree and the $K_m$-permutation graphs over a cycle.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.831-837
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• 1995

In this paper, we introduce a permutation graph over a graph G as a generalization of both a graph bundle over G and a standard permutation graph, and study a characterization of a natural isomorphism and an automorphism of permutation graphs over a graph.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.337-344
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• 1997

In this paper, we study the isomorphism problem of Cayley permutation graphs. We obtain a necessary and sufficient condition that two Cayley permutation graphs are isomrphic by a direction-preserving and color-preserving (positive/negative) natural isomorphism. The result says that if a graph G is the Cayley graph for a group $\Gamma$ then the number of direction-preserving and color-preserving positive natural isomorphism classes of Cayley permutation graphs of G is the number of double cosets of $\Gamma^\ell$ in $S_\Gamma$, where $S_\Gamma$ is the group of permutations on the elements of $\Gamma and \Gamma^\ell$ is the group of left translations by the elements of $\Gamma$. We obtain the number of the isomorphism classes by counting the double cosets.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.25-38
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• 2005

Oriented 2-factorable graphs are reduced to bouquets by permutation voltage assignment in this paper. Introducing the concept of k-class index of a permutation group, various oriented 2-factorable graphs are enumerated in this paper.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.727-734
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• 1999

Let G be a connected graph of n vertices. The problem of finding a depth-first spanning tree of G is to find a connected subgraph of G with the n vertices and n-1 edges by depth-first-search. in this paper we propose an O(n) time algorithm to solve this problem on permutation graphs.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.77-92
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• 2005

An efficient parallel algorithm is presented to find a maximum weight independent set of a permutation graph which takes O(log n) time using O($n^2$/ log n) processors on an EREW PRAM, provided the graph has at most O(n) maximal independent sets. The best known parallel algorithm takes O($log^2n$) time and O($n^3/log\;n$) processors on a CREW PRAM.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.453-467
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• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• The Transactions of the Korea Information Processing Society
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• v.6 no.8
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• pp.2124-2132
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• 1999

Given a graph G=(V,E), Ld(2,1)-labeling of G is a function f : V(G)$\longrightarrow$[0,$\infty$) such that, if v1,v2$\in$V are adjacent, $\mid$ f(x)-f(y) $\mid$$\geq$2d, and, if the distance between and is two, $\mid$ f(x)-f(y) $\mid$$\geq$d, where dG(,v2) is shortest distance between v1 and in G. The L(2,1)-labeling number (G) is the smallest number m such that G has an L(2,1)-labeling f with maximum m of f(v) for v$\in$V. This problem has been studied by Griggs, Yeh and Sakai for the various classes of graphs. In this paper, we discuss the upper-bound of ${\lambda}$ (G) for a chordal graph G and that of ${\lambda}$(G') for a permutation graph G'.

• East Asian mathematical journal
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• v.33 no.1
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• pp.67-74
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• 2017

Let k, m and t be positive integers with $m{\geq}4$ and even. It is shown that $K_{km+1(2t)}$ has a decomposition into gregarious m-cycles. Also, it is shown that $K_{km(2t)}$ has a decomposition into gregarious m-cycles if ${\frac{(m-1)^2+3}{4m}}$ < k. In this article, we make a remark that the decompositions can be circulant in the sense that it is preserved by the cyclic permutation of the partite sets, and we will exhibit it by examples.