The joint sum of graceful trees
β Scribed by De-Jun Jin; Si-Zhang Liu; Sang-Ho Lee; Hai-Lou Liu; Xi-Guan Lu; Dazhi Zhang
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 300 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
β¦ Synopsis
In this and subsequent articles, we intend to explore Rosa's conjecture that every tree is graceful [l]. We define the concept of joint sum of graceful trees and study its operational properties. We shall prove the gracefulness of a certain family of trees.
Keywords-tisak
conjecture, Graceful trees, Joint sum of graceful trees, Glue trees.
π SIMILAR VOLUMES
Koh, Rogers and Tan (Discrete Math. 25 (1979) [141][142][143][144][145][146][147][148] give a method to construct a bigger graceful tree from two graceful trees. Based upon their results, we give a new construction, which allows us to prove that the subdivision graph of a graceful tree is still a gr
The general sum-connectivity index of a graph G is defined as , where d u denotes the degree of vertex u in G, E(G) denotes the edge set of G, and Ξ± is a real number. We determine the maximum value for the general sum-connectivity indices of n-vertex trees and the corresponding extremal trees for Ξ±
The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength is the minimum number of colors needed to achieve the chromatic sum. We construct for each positive integer k a tree with strength k that has maximum degree only 2k -2. The result