ON SEPARATED GRAPHS WITH CERTAIN REGULARITY CONDITIONS

Authors
KABANOV VV MAKHNEV AA
Citation
Vv. Kabanov et Aa. Makhnev, ON SEPARATED GRAPHS WITH CERTAIN REGULARITY CONDITIONS, Sbornik. Mathematics, 187(9-10), 1996, pp. 1487-1501
Citations number
4
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Sbornik. Mathematics → ACNP
ISSN journal
10645616
Volume
187
Issue
9-10
Year of publication
1996
Pages
1487 - 1501
Database
ISI
SICI code
1064-5616(1996)187:9-10<1487:OSGWCR>2.0.ZU;2-7
Abstract
Two theorems are proved in this paper. Theorem 1 describes the connect ed mu-regular graphs without 3-claws. Necessary and sufficient conditi ons for a connected amply regular graph with mu > 1 to be separated ar e obtained in Theorem 2. A graph Gamma is said to be separated if for any vertex a in Gamma the subgraph Gamma(2)(a) contains vertices b and c at a distance 2 in Gamma(2)(a), and the mu-subgraph for any such pa ir does not intersect the neighbourhood of a.