For a group G and X a subset of G the commuting graph of G on X, denoted by \(\mathcal {C}(G,X)\), is the graph whose vertex set is X with \(x,y\in X\) joined by an edge if \(x\ne y\) and x and y commute. If the elements in X are involutions, then \(\mathcal {C}(G,X)\) is called a commuting involution graph. This paper studies \(\mathcal {C}(G,X)\) when G is a 4-dimensional projective symplectic group over a finite field and X a G-conjugacy class of involutions, determining the diameters and structure of the discs of these graphs.

中文翻译：

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四维投影辛群的通勤对合图

对于组G ^和X的一个子集ģ的通勤图ģ上X，记\（\ mathcal {C}（G，X）\） ，是其顶点集是图表X与\（X，Y \在X \）由边缘如果接合\（X \ NE Y \）和X和ÿ通勤。如果X中的元素是对合，则\（\数学{C}（G，X）\）被称为通勤对合图。当G为有限域上的4维射影辛群且X为X时，本文研究\（\数学{C}（G，X）\）一个ģ -conjugacy类对合的，确定这些曲线图的盘的直径和结构。