Peter J. Cameron

activity

20242026

collaborators

7 papers

math.CO2026

Equitable partitions of regular graphs, and perfect sets in normal Cayley graphs

R. A. Bailey, Peter J. Cameron, Sanming Zhou

An equitable partition of a graph $\Ga$ is a partition ${V_{1}, \dots, V_{m}}$ of its vertex set such that for each pair $i, j$ all vertices in $V_{i}$ have the same number of neighbo…

math.GR2025

Endomorphism and automorphism graphs of finite groups

Midhuna V Ajith, Peter J Cameron, Mainak Ghosh +1

Let $G$ be a group. The directed endomorphism graph, $\dend(G)$ of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex $a$ to the vertex $b$ if…

math.CO2025

Perfect codes in Cayley graphs of abelian groups

Peter J. Cameron, Roro Sihui Yap, Sanming Zhou

A perfect code in a graph $Γ = (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V ∖ C$ is adjacent to exactly one vertex in…

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

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…