We determine, constructively, the bandwidth of the complete k-ary tree on d levels. By rectifying an algorithm of Chung (1988), we establish B( Tk,J = rk(kd -1)/(2d( k -1)) 1. ## 1. Praeludium The bandwidth problem for a graph G is a question about numbering the vertices of G so the maximum differ
The bandwidth of the complement of A K-TREE
โ Scribed by Yuan Jinjiang; Lin Yixun
- Book ID
- 107502156
- Publisher
- SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
- Year
- 1998
- Tongue
- English
- Weight
- 189 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1005-1031
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๐ SIMILAR VOLUMES
The bandwidth B(G) of a finite simple graph G is the minimum of the quantity max{ If(x)-f(Y)I:xyC E(G)} taken over all injective integer labellings f of G. We prove that if a tree T has k leaves then B(T)<~ [k/2~. This improves the previously known upper bound B(T)<.IV(T)I/2
Let T c n be the set of the complements of trees of order n. In this paper, we characterize the unique graph whose least eigenvalue attains the minimum among all graphs in T c n .
Formulas are obtained for the number of m-cycles, y,(G, n), and the number of all cycles, -r(G, n). in the complement of a graph G with respect to the complete graph K,, in terms of the 'linear forest array' of G. Some elementary properties of these arrays are obtained. Computer results are reported