Naj bo ▫$\Gamma$▫ razdaljno regularen graf z diametrom ▫$d$▫. Za vozlišči ▫$x$▫ in ▫$y$▫ grafa ▫$\Gamma$▫ na razdalji ▫$i$▫, ▫$1 \le i \le d$▫, definiramo množice ▫$C_i = \Gamma_{i-1}(x) \cap ...\Gamma(y)$▫, ▫$A_i(x,y) = \Gamma_i(x) \cap \Gamma(y)$▫ in ▫$B_i(x,y) = \Gamma_{i+1}(x) \cap \Gamma(y)$▫. Potem rečemo, da ima graf ▫$\Gamma$▫ lastnost CAB▫$_j$▫, če je particija ▫$CAB_i(x,y) = \{C_i(x,y), A_i(x,y), B_i(x,y)\}$▫ lokalnega grafa vozlišča ▫$y$▫ ekvitabilna za vsak par ▫$x$▫ in ▫$y$▫ grafa ▫$\Gamma$▫ na razdalji ▫$i \le j$▫. Graf ▫$\Gamma$▫ ima lastnost CAB, če ima lastnost CAB▫$_d$▫. Pokažemo ekvivalentnost lastnosti CAB in lastnosti 1-homogenosti v razdaljno regularnem grafu z ▫$a_1 \ne 0$▫ in klasificiramo 1-homogene Terwilligerjeve grafe s ▫$c_2 \ge 2$▫.
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