Nonexistence of a Class of Distance-Regular Graphs

[摘要] Let $\Gamma$ denote a distance-regular graph with diameter $D \geq 3$ and intersection numbers $a_1=0, a_2 \neq 0$, and $c_2=1$. We show a connection between the $d$-bounded property and the nonexistence of parallelograms of any length up to $d+1$. Assume

[学科分类] 离散数学和组合数学

[关键词] Distance-regular graph;classical parameters;parallelogram;strongly closed subgraph;D-bounded.