1 citations · 1 across the 13 of their papers we have counts for
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On Isomorphism theorem of the Comparability Graph of Lattices
Rahul Jejurkar, Vinayak Joshi
In recent years, researchers have actively contributed to the field of graphs associated with algebraic structures and ordered structures. It is a fundamental question to ask wheth…
A Proof of the Conjecture on complemented zero-divisor graphs of semigroups
Anagha Khiste, Ganesh Tarte, Vinayak Joshi
In this paper, we are motivated by the conjectures proposed by C.~Bender \textit{et al.}, \cite{C} in 2024. We have settled the first two conjectures negatively by providing a coun…
Complemented zero-divisor graph of posets
Anagha Khiste, Ganesh Tarte, Vinayak Joshi
In this paper, we derive a set of equivalent conditions for the zero-divisor graph of a poset with to be complemented, characterizing it in terms of quasi-complement…
Cohen-Macauleyness of the Zero-Divisor Graph of a Boolean Poset
P. Waghmare, V. Joshi
In this paper, we prove that the zero-divisor graph of a Boolean poset is both well-covered and Cohen--Macaulay. Furthermore, for a poset $\mathbf{P} = \prod_{i=1}^{n} P…
Component graphs of vector spaces and zero-divisor graphs of ordered sets
Nilesh Khandekar, Peter J. Cameron, Vinayak Joshi
In this paper, nonzero component graphs and nonzero component union graphs of finite dimensional vector space are studied using the zero-divisor graph of specially constructed 0-1-…
Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures
Nilesh Khandekar, Vinayak Joshi
In this paper, we characterize chordal and perfect zero-divisor graphs of finite posets. Also, it is proved that the zero-divisor graphs of finite posets and the complement of zero…
Zero-divisor graphs of lower dismantlable lattices-II
Avinash Patil, B. N. Waphare, Vinayak Joshi
In this paper, we continue our study of the zero-divisor graphs of lower dismantlable lattices that was started in [20]. The present paper mainly deals with an Isomorphism Problem…
Zero-divisor graphs of lower dismantlable lattices-I
Avinash Patil, B. N. Waphare, Vinayak Joshi +1
In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These graphs are characterized in terms of the non-ancestor graphs of rooted trees.