MATEC Web of Conferences
Volume 31, 20152015 7th International Conference on Mechanical and Electronics Engineering (ICMEE 2015)
|Number of page(s)||3|
|Section||Computer network and communication system|
|Published online||23 November 2015|
The research of (2,1)-total labelling of trees basen on Frequency Channel Assignment problem
Department of Fundamental Courses, Ningbo Institute of Technology, Zhejiang Univ., Ningbo 315100, China
a Corresponding author: firstname.lastname@example.org
Let T be a tree, Let DΔ(T) denote the set of integers k for which there exist two distinct vertices of maximum degree of distance at k in T. The (2,1)-total labelling number of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that no two adjacent vertices have the same label, no two adjacent edges have the same label and the difference between the labels of a vertex and its incident edges is at least 2. In this paper, we prove that if T is a tree with Δ≥5 and 3,4∉DΔ(T), then T is Type 1.
© Owned by the authors, published by EDP Sciences, 2015
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