Geodesic
Exact values of girth for some graphs $D(k,q)$ and upper bounds of the order of cage
Algebra and discrete mathematics, no. 2 (2008), pp. 83-88.

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Let $q$ be a prime power and $k\in\left\{5,7,9,11\right\}$. In this paper it is shown that the girth of a graph $D\left(k,q\right)$ is equal to $k+5$. As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of $\left(r,g\right)$-cages, $r\geq 5$, $g\in\left\{10,14,16\right\}$, are given.
Keywords: Girth, Extremal.
Mots-clés : Cages 
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     author = {Piotr Pikuta},
     title = {Exact values of girth for some graphs $D(k,q)$ and upper bounds of the order of cage},
     journal = {Algebra and discrete mathematics},
     pages = {83--88},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2008_2_a4/}
}
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Piotr Pikuta. Exact values of girth for some graphs $D(k,q)$ and upper bounds of the order of cage. Algebra and discrete mathematics, no. 2 (2008), pp. 83-88. http://geodesic.mathdoc.fr/item/ADM_2008_2_a4/