3 papers
math.CO2026
On main eigenvalues of zero-divisor graphs of reduced rings
Sakshi Jain, Y. M. Borse, R. Barabde
The problem of characterizing graphs with a prescribed number of main eigenvalues is a long-standing problem in spectral graph theory. Although some constructions are known, only a…
math.CO2025
The 3-path-connectivity of the augmented cubes
S. A. Kandekar, R. Barabde, S. A. Mane
Connectivity is a cornerstone concept in graph theory, essential for evaluating the robustness of networks against failures. To better capture fault tolerance in complex systems, r…
math.CO2025
Construction and Conditions for Completely Independent Spanning Trees in Hypercubes and Regular Bipartite Graphs
R. Barabde, S. A. Mane, S. A. Kandekar
A set of \( k \) spanning trees in a graph \( G \) is called a set of \textit{completely independent spanning trees (CISTs)} if, for every pair of vertices \( x \) and \( y \), the…