4-具有2-、3-和4-二次面的效价平面图
4-valent plane graphs with 2-, 3- and 4-gonal faces
摘要：
称{ \em i-hedrite}为任意4-阶n-顶点平面图，其面仅为2-、3-和4-顶点，且为$p_2+p_3=i$ . i-多面体的边，如任何欧拉平面图的边一样，由它的{ \em中心回路}划分，即从一条边开始，在每个顶点处由与进入的边相对的边继续得到的那些。因此，任何i-hedite都是交替链接的投影，其组件对应于其中心电路。称一个i-多面体{ \em irreducible}，如果它没有{ \em rail-road}，即一个4-边形面的回路，其中每一个4-边形都与它的两个相邻边相邻。我们给出了最多有15个顶点的所有i-hedrites的列表。其他结果的例子：（i）所有的i-hedrites，这不是3-连通的，被识别。(ii)任何不可约的i-黝铜矿最多有i-2个中央回路。(iii)列出了所有没有自相交中心电路的i-hedrites。(iv)列出了i-面心石的所有对称群。
英文摘要：
Call {\em i-hedrite} any 4-valent n-vertex plane graph, whose faces are 2-, 3- and 4-gons only and $p_2+p_3=i$. The edges of an i-hedrite, as of any Eulerian plane graph, are partitioned by its {\em central circuits}, i.e. those, which are obtained by starting with an edge and continuing at each vertex by the edge opposite the entering one. So, any i-hedrite is a projection of an alternating link, whose components correspond to its central circuits. Call an i-hedrite {\em irreducible}, if it has no {\em rail-road}, i.e. a circuit of 4-gonal faces, in which every 4-gon is adjacent to two of its neighbors on opposite edges. We present the list of all i-hedrites with at most 15 vertices. Examples of other results: (i) All i-hedrites, which are not 3-connected, are identified. (ii) Any irreducible i-hedrite has at most i-2 central circuits. (iii) All i-hedrites without self-intersecting central circuits are listed. (iv) All symmetry group of i-hedrites are listed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
