论文标题
关于阿尔坦人的无效和迭代的阿尔塔斯
On the Nullity of Altans and Iterated Altans
论文作者
论文摘要
Altanisation（父型结构的高度的形成）起源于化学文献，是一种正式的装置，用于从较小的结构中构建广义冠状。图$ g $的altan表示为$ \ mathfrak {a}（g，h）$，取决于附件的选择$ h $（a Cyclic $ h $ h $ - $ g $）的顶点。从给定的一对$（g，h）$中，altan构造产生了一对$（g'，h'）$，其中$ h'$称为诱导附件集。在每个阶段使用上一步中引起的附件集的重复构造定义了迭代的altan。在这里，我们证明了基于一般父图的Altan和迭代图的无效的急剧界限：对于任何具有奇数$ h $的附件集，altan和partent的无效是相等的；对于任何$ h $和所有$ k \ geq 1 $，$ k $ -th altan的无效性与第一个相同；对于任何具有$ h $的附件设置，Altan的无效超过了父图的无效，这是由三个值$ \ {0，1，2 \} $之一。以前没有注意到过多的无效$ 2 $；对于具有由CH站点组成的天然附件套件的苯苯二甲酸酯，首先要出现$ 5 $ hexagons的父结构。根据广泛的计算，可以推测，实际上，凸苯甲衣的altan没有过多的$ 2 $。
Altanisation (formation of the altan of a parent structure) originated in the chemical literature as a formal device for constructing generalised coronenes from smaller structures. The altan of graph $G$, denoted $\mathfrak{a}(G, H)$, depends on the choice of attachment set $H$ (a cyclic $h$-tuple of vertices of $G$). From a given pair $(G, H)$, the altan construction produces a pair $(G', H')$, where $H'$ is called the induced attachment set. Repetition of the construction, using at each stage the attachment set induced in the previous step, defines the iterated altan. Here, we prove sharp bounds for the nullity of altan and iterated altan graphs based on a general parent graph: for any attachment set with odd $h$, nullities of altan and parent are equal; for any $h$ and all $k \geq 1$, the $k$-th altan has the same nullity as the first; for any attachment set with even $h$, the nullity of the altan exceeds the nullity of the parent graph by one of the three values $\{0, 1, 2\}$. The case of excess nullity $2$ has not been noticed before; for benzenoids with the natural attachment set consisting of the CH sites, it occurs first for a parent structure with $5$ hexagons. On the basis of extensive computation, it is conjectured that in fact no altan of a convex benzenoid has excess nullity $2$.
