Vol. 8 No. 1 (2024): Vol 8, Iss 1, Year 2024
Articles

# Topological indices of join graph of zero divisor graphs of direct product of three finite fields

R. K. Talreja College of Arts, Science and Commerce, Ulhasnagar, Maharashtra, India
Nithya Sai Narayana
Department of Mathematics, University of Mumbai, Mumbai, Maharashtra, India
Published June 30, 2024
Keywords
• Zero divisor graph, Join graph, Weiner index, degree based topological indices, eccentricity based topological indices.
How to Cite
Subhash Mallinath Gaded, & Nithya Sai Narayana. (2024). Topological indices of join graph of zero divisor graphs of direct product of three finite fields. Journal of Computational Mathematica, 8(1), 015-027. https://doi.org/10.26524/cm182

### Abstract

In this paper, we calculate the Weiner index, some degree-based topological indices, and some eccentricity-based topological indices of Join graph of Γ(F1 ×F2 ×F3) and Γ(J1 ×J2 ×J3), where F1, F2, F3, J1, J2, J3 are finite fields of order at least two.  The vertex set of Γ(F1×F2×F3) (Γ(J1×J2 ×J3)) is Z(F1 ×F2 ×F3) (Z(J1 ×J2 ×J3)), the set of non-zero zero divisors, and two distinct vertices (x1, x2, x3), (y1, y2, y3) are adjacent if and  only  if  (x1, x2, x3) · (y1, y2, y3)  = (0, 0, 0), the additive identity of the ring F1 × F2 × F3 (J1 × J2 × J3). The vertex set of Join graph Γ(F1 × F2 × F3) + Γ(J1 × J2 × J3) is V (Γ(F1 × F2 × F3)) ∪ V (Γ(J1 × J2 × J3)) and edge set is E(Γ(F1 × F2 × F3))   ∪  E(Γ(J1 × J2 × J3))  ∪  {(x1, x2, x3) · (y1, y2, y3) : (x1, x2, x3) ∈ V (Γ(F1 × F2 × F3)), (y1, y2, y3) ∈ V (Γ(J1 × J2 × J3))}.