In this work, we study the cellular decomposition of S induced by a filling pair curves v and w, \(Dec_{v,w}(S) = {\setminus } (v \cup w)\), its connection to distance function d(v, w) in curve graph closed orientable surface genus g. Building on work Leasure, efficient geodesics were introduced first author joint with Margalit Menasco 2016, giving an algorithm that begins non-separating determ...

We prove that there are intersection graphs of axis-aligned boxes in R3 and straight lines have arbitrarily large girth chromatic number.

This study was carried out to analyze the variations of Benzene, Toluene, and para- Xylene (BTp-X) present in the urban air of Delhi. These pollutants can enter into the human body through various pathways like inhalation, oral and dermal exposure posing adverse effects on human health. Keeping in view of the above facts, six different locations of Delhi were selected for the study during summe...

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...