The irregularity of two types of trees

Yang Liu (1) , Jianxi Li (1) , Wai Chee (2)

1 School of Mathematics and Statistics, Minnan Normal University
2 Department of Mathematics

The irregularity of a graph G is defined as the sum of weights |d(u) − d(v)| of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, some structural properties on trees with maximum (or minimum) irregularity among trees with given degree sequence and trees with given branching number are explored, respectively. Moreover, the corresponding trees with maximum (or minimum) irregularity are also found, respectively.

Mots clés: Irregularity; trees; degree sequence; branching number

Domaines: Mathématiques [math]; Optique [physics.optics]

Yang Liu, Jianxi Li, Wai Chee. The irregularity of two types of trees. 2015. ⟨hal-01166543⟩