3 papers
math.CO2025
On the strong metric dimension of the complement of the zero-divisor graph of a lattice
Pravin Gadge, Vinayak Joshi
In this paper, we compute the strong metric dimension of the complement of the zero-divisor graph of the blow-up of a Boolean lattice. Using these results, we calculate the strong…
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…
math.CO2024
On the strong metric dimension of the zero-divisor graph of a lattice
Pravin Gadge, Vinayak Joshi
In this paper, the generalized blow-up of a Boolean lattice using finite chains is introduced. Also, we compute the strong metric dimension of the zero-diviso…