A well-known technique to construct regular graphs with girth 5 is the amalgamation into the incidence graphs ${\mathcal{C}}_q$ and ${\mathcal{L}}_q$, elliptic semiplanes of type $C$ and $L$ respectively, where $q$ is a prime power. The case $q$ odd has extensively been studied by means of amalgamations into ${\mathcal{L}}_q.$ In this paper we provide new families of small regular graphs of girth 5 constructed by amalgamation into ${\mathcal{C}}_q$ using finite fields of even order.

中文翻译：

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椭圆半平面类型的周长5的正则图 $C$

构造周长为5的正则图的一项众所周知的技术是将其合并到入射图中 ${\mathcal{C}}_q$ 和 ${\mathcal{大号}}_q$的椭圆半平面 $C$ 和 $\mathrm{大号}$ 分别在哪里 $q$是主要力量。案子$q$ 奇特通过合并的方法被广泛研究。 ${\mathcal{大号}}_q。$ 在本文中，我们提供了通过合并为第5周长的小型正则图的新族 ${\mathcal{C}}_q$ 使用偶数阶的有限域。