DIAMETER OF COMMUTING GRAPHS OF SYMPLECTIC ALGEBRAS
2019 ◽
Vol 100
(3)
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pp. 419-427
Keyword(s):
Let $F$ be an algebraically closed field of characteristic $0$ and let $\operatorname{sp}(2l,F)$ be the rank $l$ symplectic algebra of all $2l\times 2l$ matrices $x=\big(\!\begin{smallmatrix}A & B\\ C & -A^{t}\end{smallmatrix}\!\big)$ over $F$, where $A^{t}$ is the transpose of $A$ and $B,C$ are symmetric matrices of order $l$. The commuting graph $\unicode[STIX]{x1D6E4}(\operatorname{sp}(2l,F))$ of $\operatorname{sp}(2l,F)$ is a graph whose vertex set consists of all nonzero elements in $\operatorname{sp}(2l,F)$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=yx$. We prove that the diameter of $\unicode[STIX]{x1D6E4}(\operatorname{sp}(2l,F))$ is $4$ when $l>2$.
Keyword(s):
1959 ◽
Vol 14
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pp. 223-234
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Keyword(s):
2013 ◽
Vol 89
(2)
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pp. 234-242
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2014 ◽
Vol 35
(7)
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pp. 2242-2268
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2011 ◽
Vol 11
(2)
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pp. 221-271
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1976 ◽
Vol 59
(1)
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pp. 29-29
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Keyword(s):
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2008 ◽
Vol 4
(1)
◽
pp. 91-100
1968 ◽
Vol 9
(2)
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pp. 146-151
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