Vipul Kakkar

activity

20242026

collaborators

4 papers

math.GR2026

Impartial games on two finite Groups

Ratan Lal, Muskan, Vipul Kakkar

In this paper, we study impartial achievement games and impartial avoidance games introduced by Anderson and Harary. Using the criteria of maximal subgroups, we study the game for…

math.GR2025

Determinant for automorphisms of semidirect product of groups

Ratan Lal, Alka Choudhary, Vipul Kakkar

A description of the endomorphisms of semidirect products of two groups as a group of $2 \times 2$ matrices of maps is already known. Using this description, we have studied the con…

math.CO2025

Line Graph Characterization of Cyclic Subgroup Graph

Siddharth Malviy, Vipul Kakkar, Swapnil Srivastava

The cyclic subgroup graph $I^ (G)$ of a group $G$ is the simple undirected graph with cyclic subgroups as a vertex set and two distinct vertices $H_{1}$ and $H_{2}$ are adjacent if an…

math.CO2024

The Minimal (Edge) Connectivity of Some Graphs of Finite Groups

Siddharth Malviy, Vipul Kakkar

In this paper, we classify all the finite groups $G$ such that the commuting graph $I^_{C} (G)$ , order-sum graph $I^_{O S} (G)$ and non-inverse graph $I^_{N I} (G)$ are minimally edge con…