The study of odd graceful and odd strongly harmonious for bipartite graph

Growing Graceful and Harmonious Trees

We describe symbolic constructions for listing and enumerating graphs having the same induced edge label sequence. We settle in the affirmative R. Whitty's [W08] conjectured existence of determinantal constructions for listing and enumerating gracefully labeled trees. We conclude the paper with a description of a new graceful labeling algorithm.

On d-graceful labelings

In this paper we introduce a generalization of the well known concept of a graceful labeling. Given a graph G with e=dm edges, we call d-graceful labeling of G an injective function from V(G) to the set {0,1,2,..., d(m+1)-1} such that {|f(x)-f(y)| | [x,y]\in E(G)} ={1,2,3,...,d(m+1)-1}-{m+1,2(m+1),...,(d-1)(m+1)}. In the case of d=1 and of d=e we find the classical notion of a graceful labeling and of an odd graceful labeling, respectively. Also, we call d-graceful α-labeling of a bipartite graph G a d-graceful labeling of G with the property that its maximum value on one of the two bipartite …

图的奇优美色数的上界

Upper bounds on the odd graceful chromatic number of graphs

本文研究二部图的奇优美色数，给出若干仅依赖顶点数或其二部划分相关图色数的新上界。

A Note on Set Graceful Labeling of Graphs

We settle affirmatively a conjecture posed in [S. M. Hegde, Set colorings of graphs, European Journal of Combinatorics 30 (4) (2009), 986--995]: If some subsets of a set X are assigned injectively to all vertices of a complete bipartite graph G such that the collection of all sets, each of which is the symmetric difference of the sets assigned to the ends of some edge, is the set of all nonempty subsets of X, then G is a star.

Moore图及其他图的无线电优美性

Radio gracefulness of Moore graphs and beyond

该研究围绕无线电频率分配建模的无线电优美标号问题，确定了Moore图等多类低直径高性能计算相关图的无线电优美性，证明了直径3二部图的相关充要条件并算出部分笼图的无线电数。

关于图的$k$-超优美标号

On $k$-Super Graceful Labeling of Graphs

该文研究图的$k$-超优美标号问题，给出相关一般性质，得到多类（完全）二部、三部图$k$-超优美性的充分条件，且证明部分条件同时是必要的。