Department of Mathematics
(2,1)-total labeling of trees with large maximum degree
© 2015 Elsevier B.V. A k-(2, 1)-total labeling of a graph G is to label the vertices and the edges of G using integers from 0 to k such that all adjacent vertices as well as edges receive different labels, and the difference between the labels of a vertex and its incident edges is at least 2. The (2,1)-total labeling number λ2t(G) is the smallest integer k such that G has a k-(2, 1)-total labeling. It is known that λ2t(T), where T is a tree with maximum degree Δ, equals to either Δ+1 or Δ+2. In this paper, we provide a sufficient condition for a tree T to have λ2t(T)=Δ+1 when Δ≥9.
(2, 1) -total labeling, Maximum degree, Tree
Source Publication Title
Discrete Applied Mathematics
Chen, Dong, Wai Chee Shiu, Qiaojun Shu, Pak Kiu Sun, and Weifan Wang. "(2,1)-total labeling of trees with large maximum degree." Discrete Applied Mathematics 187 (2015): 61-69.