The harmonious chromatic number of complete r-ary trees

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 - https://www.scopus.com/pages/publications/0345884732

M3 - Article

AN - SCOPUS:0345884732

SN - 0012-365X

VL - 203

SP - 83

EP - 99

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -