R. K. Nath

activity

20102026

most citedFinite groups whose commuting graphs are integral

12 citations · 42 across the 47 of their papers we have counts for

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Showing 2024Show all

11 papers · 1 filter

math.GR2024

On a bipartite graph defined on groups

Shrabani Das, Ahmad Erfanian, Rajat Kanti Nath

Let $G$ be a group and $L (G)$ be the set of all subgroups of $G$ . We introduce a bipartite graph $B (G)$ on $G$ whose vertex set is the union of two sets $G \times G$ and…

math.GR2024

Commuting Conjugacy Class Graphs of Finite Groups and the Hansen-Vukičević Conjecture

Shrabani Das, Rajat Kanti Nath, Yilun Shang

In this work, we compute the first and second Zagreb indices for the commuting conjugacy class graphs associated with finite groups. We identify multiple classes of finite groups w…

math.GR2024

Engel and co-Engel graphs of finite groups

Peter J. Cameron, Rishabh Chakraborty, Rajat Kanti Nath +1

Let $G$ be a group. Associate a directed graph $E (G)$ (called the Engel digraph of $G$ ) with $G$ whose vertex set is $G$ , with an arc $(x, y)$ if $[y,_{k} x] = 1$ for some posi…

math.CO2024

Main functions and the spectrum of super graphs

G. Arunkumar, Peter J. Cameron, R. Ganeshbabu +1

Let A be a graph type and B an equivalence relation on a group $G$ . Let $[g]$ be the equivalence class of $g$ with respect to the equivalence relation B. The B superA graph of $G$ …

math.GR2024★ 1 cited

Super commuting graphs of finite groups and their Zagreb indices

Shrabani Das, Rajat Kanti Nath

Let $B$ be an equivalence relation defined on a finite group $G$ . The $B$ super commuting graph on $G$ is a graph whose vertex set is $G$ and two distinct vertices $g$ and $h$ are…

math.GR2024

A survey on conjugacy class graphs of groups

P. J. Cameron, F. E. Jannat, R. K. Nath +1

There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group $G$ and adjacency is defined by properties of the e…

math.GR2024

Common neighborhood (signless) Laplacian spectrum and energy of CCC-graph

Firdous Ee Jannat, Rajat Kanti Nath

In this paper, we consider commuting conjugacy class graph (abbreviated as CCC-graph) of a finite group $G$ which is a graph with vertex set ${x^{G} : x \in G ∖ Z (G)}$ (whe…

math.GR2024

Common neighborhood Laplacian and signless Laplacian spectra and energies of commuting graphs

Firdous Ee Jannat, Rajat Kanti Nath

In this paper, we compute common neighbourhood Laplacian spectrum, common neighbourhood signless Laplacian spectrum and their respective energies of commuting graph of some finite…

math.CO2024

Common neighborhood energies and their relations with Zagreb index

Firdous Ee Jannat, Rajat Kanti Nath, Kinkar Chandra Das

In this paper we establish connections between common neighborhood Laplacian and common neighborhood signless Laplacian energies and the first Zagreb index of a graph $G$ …

math.GR2024

Super graphs on groups, II

G. Arunkumar, Peter J. Cameron, Rajat Kanti Nath

In an earlier paper, the authors considered three types of graphs, and three equivalence relations, defined on a group, viz.\ the power graph, enhanced power graph, and commuting g…

math.GR2024

Characterization of commuting graphs of finite groups having small genus

Shrabani Das, Deiborlang Nongsiang, Rajat Kanti Nath

In this paper we first show that among all double-toroidal and triple-toroidal finite graphs only $K_{8} ⊔ 9 K_{1}$ , $K_{8} ⊔ 5 K_{2}$ , $K_{8} ⊔ 3 K_{4}$ , $K_{8} ⊔ 9 K_{3}$ , $K_8\s…