• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.65-75
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• 2007

A graph G is self-complementary (sc) if it is isomorphic to its complement. G is perfect if for all induced subgraphs H of G, the chromatic number of H (denoted ${\chi}$(H)) equals the number of vertices in the largest clique in H (denoted ${\omega}$(H)). An sc graph which is also perfect is known as sc perfect graph. A comparability graph is an undirected graph if it can be oriented into transitive directed graph. An sc comparability (scc) is clearly a subclass of sc perfect graph. In this paper we show that no two non-isomorphic scc graphs with n vertices each, (n<13) have same spectrum, and that the smallest positive integer for which there exists hyper-energetic scc graph is 13.

• The Journal of Information Technology and Database
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• v.3 no.1
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• pp.97-108
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• 1996

In this paper we obtain several function defined on finite partially ordered sets(posets) which may indicate constraints of comparability on sets of teams(tasks, etc.) for which evaluation is computationally simple, a relatively rare condition in graph-based algorithms. Using these functions a set of numerical coefficients and associated distributions obtained from a computer simulation of certain families of random graphs is determined. From this information estimates may be made as to the actual linearity of complicated posets. Applications of these ideas is to all areas where obtaining rankings from partial information in rational ways is relevant as in, e.g., team_, scaling_, and scheduling theory as well as in theoretical computer science. Theoretical consideration of special and desirable properties of various functions is provided permitting judgment concerning sensitivity of these functions to changes in parameters describing (finite) posets.