Title: Trees Which Admit No alpha-labelings
Authors: Shiue, Chin-Lin
Lu, Hui-Chuan
Department of Applied Mathematics
Keywords: alpha-labeling matrix;matrix graph;comet
Issue Date: 1-Jan-2012
Abstract: In this paper, we study the existence of alpha-labelings for trees by means of particular (0, 1)-matrices called alpha-labeling matrices. It is shown that each cornet S(k,q) admits no alpha-labelings whenever k > 4(q - 1) and q >= 2. We also give the sufficient conditions for the nonexistence of alpha-labelings for trees of diameter at most six. This extends a result of Rosa's. As a consequence, we prove that S(k,3) has an alpha-labeling if and only if k <= 4.
URI: http://hdl.handle.net/11536/15343
ISSN: 0381-7032
Volume: 103
Begin Page: 453
End Page: 463
Appears in Collections:Articles