We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result a...We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].展开更多
A graph is equitably k-colorable if its vertices can be partitioned into k independent sets of as near equal sizes as possible.In this paper,we give new methods to prove some known results of equitable coloring of com...A graph is equitably k-colorable if its vertices can be partitioned into k independent sets of as near equal sizes as possible.In this paper,we give new methods to prove some known results of equitable coloring of complete r-partite Graphs.展开更多
In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tr...In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.展开更多
With its comprehensive application in network information engineering (e.g. dynamic spectrum allocation under different distance constraints) and in network combination optimization (e.g. safe storage of deleterious m...With its comprehensive application in network information engineering (e.g. dynamic spectrum allocation under different distance constraints) and in network combination optimization (e.g. safe storage of deleterious materials), the graphs ’ cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K(m, n)-A (AE(K(m, n)) and |A|≥2) is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K(m,n)-A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.展开更多
文摘We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].
文摘A graph is equitably k-colorable if its vertices can be partitioned into k independent sets of as near equal sizes as possible.In this paper,we give new methods to prove some known results of equitable coloring of complete r-partite Graphs.
文摘In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.
基金Natural Science Foundation of Fujian, China (No.S0650011)
文摘With its comprehensive application in network information engineering (e.g. dynamic spectrum allocation under different distance constraints) and in network combination optimization (e.g. safe storage of deleterious materials), the graphs ’ cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K(m, n)-A (AE(K(m, n)) and |A|≥2) is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K(m,n)-A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.
