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math.GR2025
On the deep commuting graph of a finite group
Sumana Hatui, Sanjay Mukherjee, Kamal Lochan Patra
Let be a finite group and let be a Schur cover of . The deep commuting graph of is a simple graph with vertex set , where two distinct vertices a…
math.GR2022
On the super graphs and reduced super graphs of some finite groups
Sandeep Dalal, Sanjay Mukherjee, Kamal Lochan Patra
For a finite group , let be an equivalence (equality, conjugacy or order) relation on and let be a (power, enhanced power or commuting) graph with vertex set . Th…
math.GR2021
Characterizing finite nilpotent groups associated with a graph theoretic equality
Ramesh Prasad Panda, Kamal Lochan Patra, Binod Kumar Sahoo
The power graph of a group is the simple graph whose vertices are the group elements and two vertices are adjacent whenever one of them is a positive power of the other. We charact…