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. © 2016 Elsevier B.V.

ASHOK DAS

Pure Mathematics

R CHAKRABORTY

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Discrete Applied Mathematics

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. © 2015 Elsevier B.V. All rights reserved.

Fulltext

Discrete Mathematics

Forbidden substructure for interval digraphs/bigraphs

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 adjacent when the corresponding intervals intersect. In this paper, we introduce the notion of astral triple of edges and along the lines of characterization of interval graphs via the absence of asteroidal triple of vertices we characterize proper interval bigraphs via the absence of astral triple of edges. We also characterize proper interval bigraphs in terms of dominating pair of vertices as defined by Corneil et al. Tucker characterized proper circular arc graphs in terms of circularly compatible 1's of adjacency matrices. Sen and Sanyal characterized adjacency matrices of proper interval bigraphs in terms of monotone consecutive arrangement. We have shown an interrelation between these two concepts. © 2015 Kalasalingam University.

Journal	Data powered by TypesetDiscrete Applied Mathematics
Publisher	Data powered by TypesetElsevier B.V.
ISSN	0166-218X
Open Access	No