TY - JOUR
T1 - The harmonious chromatic number of complete r-ary trees
AU - Edwards, K.
N1 - Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 1999
Y1 - 1999
N2 - A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring. We define Q(m) to be the least positive integer k such that () = m. Then h(G) = Q(m) for any graph G with m edges. We consider the complete r-ary tree of height H, denoted T. We show that for any r = 2, H = 3, if m is the number of edges of T, then h(T) = Q(m), except that h(T) = 7.
AB - A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring. We define Q(m) to be the least positive integer k such that () = m. Then h(G) = Q(m) for any graph G with m edges. We consider the complete r-ary tree of height H, denoted T. We show that for any r = 2, H = 3, if m is the number of edges of T, then h(T) = Q(m), except that h(T) = 7.
UR - http://www.scopus.com/inward/record.url?scp=0345884732&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0345884732
SN - 0012-365X
VL - 203
SP - 83
EP - 99
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -