3 papers
math.CO2026
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…
math.CO2026
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-complemen…
math.CO2025
Counter-example to Conjectures on Complemented Zero-Divisor Graphs of Semigroups
Anagha Khiste, Ganesh Tarte, Vinayak Joshi
In this paper, we are motivated by two conjectures proposed by C. Bender et al.\ in 2024, which have remained open questions. The first conjecture states that if the complemented z…