caa a22 4500 475807723 CHVBK 20180406123751.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1023/A:1008339728235 doi (NATIONALLICENCE)springer-10.1023/A:1008339728235 A Local Approach to 1-Homogeneous Graphs [Elektronische Daten] [Aleksandar Jurivsic, Jack Koolen] Let Г bea distance-regular graph with diameter d. For vertices x and y of Г at distancei, 1 ≤ i ≤ d, we define the setsC i(x,y) = Гi−1(x) ⋂ Г(y), A i (x,y) = Г i (x) ⋂ Г(y) and B i (x,y) = Г i+1(x) ⋂ Г(y).Then we say Г has the CABj property,if the partition CAB i (x,y) = {C i (x,y),A i (x,y),B i (x,y)}of the local graph of y is equitable for each pairof vertices x and y of Гat distance i ≤ j. We show that in Гwith the CABj property then the parameters ofthe equitable partitions CAB i(x,y) do not dependon the choice of vertices x and y atdistance i for all i ≤ j. The graphГ has the CAB property if it has the CAB d property. We show the equivalence of the CAB property and the1-homogeneous property in a distance-regular graph with a 1 ≠0. Finally, we classify the 1-homogeneous Terwilligergraphs with c 2 Г 2. Kluwer Academic Publishers, 2000 Distance-regular graphs nationallicence equitable partitions nationallicence 1-homogeneous nationallicence locally strongly-regular nationallicence Jurivsic Aleksandar Nova Gorica Polytechnic, Vipavska 13, p.p. 301, Nova Gorica, Slovenia aut Koolen Jack Centrum voor Wiskunde en Informatica, Kruislaan, 413, NL-1098SJ, Amsterdam, The Netherlands aut Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 127-147 0925-1022 21:1-3<127 2000 21 10623 https://doi.org/10.1023/A:1008339728235 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008339728235 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jurivsic Aleksandar Nova Gorica Polytechnic, Vipavska 13, p.p. 301, Nova Gorica, Slovenia aut NATIONALLICENCE 700 1- Koolen Jack Centrum voor Wiskunde en Informatica, Kruislaan, 413, NL-1098SJ, Amsterdam, The Netherlands aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 127-147 0925-1022 21:1-3<127 2000 21 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer