On the strong metric dimension of the zero-divisor graph of a lattice

P Gadge, V Joshi - arXiv preprint arXiv:2409.05146, 2024 - arxiv.org
In this paper, the generalized blow-up of a Boolean lattice $ L\cong\textbf {2}^ n $ using finite
chains is introduced. Also, we compute the strong metric dimension of the zero-divisor graph …

Eulerian and pancyclic zero-divisor graphs of ordered sets

N Khandekar, V Joshi - AKCE International Journal of Graphs and …, 2024 - Taylor & Francis
In this paper, we determine when the zero-divisor graph of a special class of a finite
pseudocomplemented poset is Eulerian. Also, we deal with Hamiltonian, vertex pancyclic …

On the comaximal graph of a ring

P Gadge, N Khandekar, V Joshi - AKCE International Journal of …, 2024 - Taylor & Francis
In this paper, we prove that the study of the comaximal graph of a finite commutative ring
with identity is the same as the study of the zero-divisor graph of the specially constructed …

Total coloring of graphs associated with algebraic structures and ordered structures

N Khandekar, V Joshi - Indian Journal of Pure and Applied Mathematics, 2023 - Springer
In this paper, we prove that the zero-divisor graphs of finite posets and the complement of
zero-divisor graphs of finite 0-distributive posets satisfy the Total Coloring Conjecture. These …

Total graph of a lattice

P Gadge, V Joshi - Indian Journal of Pure and Applied Mathematics, 2024 - Springer
In this paper, we prove that the study of the subgraph T (Z∗(L)) of the total graph T (L) of a
lattice L is essentially the study of the zero-divisor graph of a poset. Also, we prove that the …