所有最多8个节点的图都是2区间PCG
All Graphs with at most 8 nodes are 2-interval-PCGs
AI总结：
本文证明所有最多8个节点的图都是2区间PCG，推进了确定最小n值的研究。
摘要：
一个图G是多区间PCG，若存在一个边加权树T和非负实数半轴上的不相交区间，使得每个节点唯一对应T的叶节点，且两个节点之间有边当且仅当它们对应的叶节点在T中的加权距离落在任一区间内。若区间数为k，则称为k区间PCG。已知2区间PCG不包含所有图，已知最小的不在该类中的图有135个节点。本文证明所有最多8个节点的图都是2区间PCG，从而推进了确定最小n值的研究。
英文摘要：
A graph G is a multi-interval PCG if there exist an edge weighted tree T with non-negative real values and disjoint intervals of the non-negative real half-line such that each node of G is uniquely associated to a leaf of T and there is an edge between two nodes in G if and only if the weighted distance between their corresponding leaves in T lies within any such intervals. If the number of intervals is k, then we call the graph a k-interval-PCG; in symbols, G = k-interval-PCG (T, I1, . . . , Ik). It is known that 2-interval-PCGs do not contain all graphs and the smallest known graph outside this class has 135 nodes. Here we prove that all graphs with at most 8 nodes are 2-interval-PCGs, so doing one step towards the determination of the smallest value of n such that there exists an n node graph that is not a 2-interval-PCG.
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。
