Author

# Ashok Kumar Das

Bio: Ashok Kumar Das is an academic researcher from University of Calcutta. The author has contributed to research in topics: Bigraph & Vertex (geometry). The author has an hindex of 3, co-authored 6 publications receiving 17 citations.

##### Papers

More filters

••

TL;DR: The method finds hitherto existing forbidden substructures for interval matrices via a more concise statement, as well as a new example showing that these substructureures are not exhaustive.

Abstract: An interval matrix is the adjacency matrix of an interval digraph or equivalently the biadjacency matrix of an interval bigraph. In this paper we investigate the forbidden substructures of an interval bigraph. Our method finds hitherto existing forbidden substructures for interval matrices, and via a more concise statement, as well as a new example showing that these substructures are not exhaustive.

8 citations

••

TL;DR: The notion of astral triple of edges is introduced and along the lines of characterization of interval graphs via the absence of asteroidal triple of vertices the proper interval bigraphs are characterized via the presence of astrals.

Abstract: A proper interval bigraph is a bigraph where to each vertex we can assign a closed interval such that the intervals can be chosen to be inclusion free and vertices in the opposite partite sets are ...

5 citations

••

08 Feb 2015TL;DR: This paper characterize proper interval bigraphs and proper circular arcbigraphs using two linear orderings of their vertex set.

Abstract: An interval bigraph B is a proper interval bigraph if there is an interval representation of B such that no interval of the same partite set is properly contained in the other. Similarly a circular arc bigraph B is a proper circular arc bigraph if there is a circular arc representation of B such that no arc of the same partite set is properly contained in the other. In this paper, we characterize proper interval bigraphs and proper circular arc bigraphs using two linear orderings of their vertex set.

3 citations

••

TL;DR: It is shown that a graph is a circular arc graph if and only if the corresponding symmetric digraph with loops is aCircular arc digraphs are characterized using circular ordering of their edges.

Abstract: In this paper, we have shown that a graph is a circular arc graph if and only if the corresponding symmetric digraph with loops is a circular arc digraph. We characterize circular arc digraphs and circular arc graphs using circular ordering of their edges. We also characterize a circular arc graph as a union of an interval graph and a threshold graph. Finally, we characterize proper interval bigraphs and proper circular arc bigraphs using two linear orderings of their vertex set.

2 citations

••

19 Dec 2016TL;DR: A new approach of finding the forbidden subgraphs of bigraphs of Ferrers dimension 2 when it contains a strong bisimplicial edge is presented.

Abstract: A bipartite graph B with bipartion X, Y is called a Ferrers bigraph if the neighbor sets of the vertices of X (or equivalently Y) are linearly ordered by set inclusion. The Ferrers dimension of B is the minimum number of Ferrers bigraphs whose intersection is B. In this paper we present a new approach of finding the forbidden subgraphs of bigraphs of Ferrers dimension 2 when it contains a strong bisimplicial edge.

1 citations

##### Cited by

More filters

••

TL;DR: A minimal forbidden submatrix characterization for the circularly compatible ones property in arbitrary matrices and a linear-time recognition algorithm for the same property are given.

Abstract: In 1969, Tucker characterized proper circular-arc graphs as those graphs whose augmented adjacency matrices have the circularly compatible ones property. Moreover, he also found a polynomial-time a...

3 citations

••

08 Feb 2015TL;DR: This paper characterize proper interval bigraphs and proper circular arcbigraphs using two linear orderings of their vertex set.

Abstract: An interval bigraph B is a proper interval bigraph if there is an interval representation of B such that no interval of the same partite set is properly contained in the other. Similarly a circular arc bigraph B is a proper circular arc bigraph if there is a circular arc representation of B such that no arc of the same partite set is properly contained in the other. In this paper, we characterize proper interval bigraphs and proper circular arc bigraphs using two linear orderings of their vertex set.

3 citations

••

TL;DR: It is shown that a graph is a circular arc graph if and only if the corresponding symmetric digraph with loops is aCircular arc digraphs are characterized using circular ordering of their edges.

Abstract: In this paper, we have shown that a graph is a circular arc graph if and only if the corresponding symmetric digraph with loops is a circular arc digraph. We characterize circular arc digraphs and circular arc graphs using circular ordering of their edges. We also characterize a circular arc graph as a union of an interval graph and a threshold graph. Finally, we characterize proper interval bigraphs and proper circular arc bigraphs using two linear orderings of their vertex set.

2 citations

•

TL;DR: In this article, the domination number of a special type of interval catch digraph (ICD) family for one-dimensional data in a randomized setting was derived for testing uniformity.

Abstract: We consider a special type of interval catch digraph (ICD) family for one-dimensional data in a randomized setting and propose its use for testing uniformity. These ICDs are defined with an expansion and a centrality parameter, hence we will refer to this ICD as parameterized ICD (PICD). We derive the exact (and asymptotic) distribution of the domination number of this PICD family when its vertices are from a uniform (and non-uniform) distribution in one dimension for the entire range of the parameters; thereby determine the parameters for which the asymptotic distribution is non-degenerate. We observe jumps (from degeneracy to non-degeneracy or from a non-degenerate distribution to another) in the asymptotic distribution of the domination number at certain parameter combinations. We use the domination number for testing uniformity of data in real line, prove its consistency against certain alternatives, and compare it with two commonly used tests and three recently proposed tests in literature and also arc density of this ICD and of another ICD family in terms of size and power. Based on our extensive Monte Carlo simulations, we demonstrate that domination number of our PICD has higher power for certain types of deviations from uniformity compared to other tests.

2 citations