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…

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…