Geodesic
Commuting involution graphs for 3-dimensional unitary groups
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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For a group $G$ and $X$ a subset of $G$ the commuting graph of $G$ on $X$, denoted by $\cal{C}(G,X)$, is the graph whose vertex set is $X$ with $x,y\in X$ joined by an edge if $x\neq y$ and $x$ and $y$ commute. If the elements in $X$ are involutions, then $\cal{C}(G,X)$ is called a commuting involution graph. This paper studies $\cal{C}(G,X)$ when $G$ is a 3-dimensional projective special unitary group and $X$ a $G$-conjugacy class of involutions, determining the diameters and structure of the discs of these graphs.
DOI : 10.37236/590
Classification : 05C12, 20E99 
@article{10_37236_590,
     author = {Alistaire Everett},
     title = {Commuting involution graphs for 3-dimensional unitary groups},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/590},
     zbl = {1217.05083},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/590/}
}
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Alistaire Everett. Commuting involution graphs for 3-dimensional unitary groups. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/590

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