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1.
On adjacent-vertex-distinguishing total coloring of graphs   总被引：32，自引：0，他引：32
In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number of some graphs such as cycle, complete graph, complete bipartite graph, fan, wheel and tree.  相似文献
2.
A Note on Adjacent Strong Edge Coloring of K（n,m）   总被引：11，自引：0，他引：11
In this paper, we prove that the adjacent strong edge chromatic number of a graph K（n,m） is n ＋ 1, with n ≥ 2, m ≥ 1.  相似文献
3.

k-正常边染色法f,若满足任两个不同点的关联边色集不同,则称f为G的k-点可区别边染色,简记为k-VDEC of G,并称最小的k为G的点可区别边色数;对k-VDEC若再满足任意两色的边数之差不超过1,则称f为G的点可区别均匀边染色,简记为k-VDEEC of G,并称最小的k为G的点可区别均匀边色数．本文得到了图等阶的路和路,路和圈,圈和圈的联图的点可区别均匀边色数．  相似文献
4.
D(β)-vertex-distinguishing total coloring of graphs   总被引：2，自引：0，他引：2
A new concept of the D(β)-vertex-distinguishing total coloring of graphs, i.e., the proper total coloring such that any two vertices whose distance is not larger thanβhave different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it, is proposed in this paper. The D(2)-vertex-distinguishing total colorings of some special graphs are discussed, meanwhile, a conjecture and an open problem are presented.  相似文献
5.
D(β)-vertex-distinguishing total coloring of graphs   总被引：1，自引：0，他引：1
A new concept of the D(β)-vertex-distinguishing total coloring of graphs, i.e., the proper total coloring such that any two vertices whose distance is not larger than β have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it, is proposed in this paper. The D(2)-vertex-distinguishing total colorings of some special graphs are discussed, meanwhile, a conjecture and an open problem are presented.  相似文献
6.
Suppose that $$G$$ is a finite group and $$H$$ , $$K$$ are subgroups of $$G$$ . We say that $$H$$ is weakly closed in $$K$$ with respect to $$G$$ if, for any $$g \in G$$ such that $$H^{g}\le K$$ , we have $$H^{g}=H$$ . In particular, when $$H$$ is a subgroup of prime-power order and $$K$$ is a Sylow subgroup containing it, $$H$$ is simply said to be a weakly closed subgroup of $$G$$ or weakly closed in $$G$$ . In the paper, we investigate the structure of finite groups by means of weakly closed subgroups.  相似文献
7.
In this paper, an infinite horizon $H_2/H_\infty$ control problem is addressed for a broad class of discrete-time Markov jump systems with ( $x,u,v$ )-dependent noises. First of all, under the condition of exact detectability, the stochastic Popov–Belevich–Hautus (PBH) criterion is utilized to establish an extended Lyapunov theorem for a generalized Lyapunov equation. Further, a necessary and sufficient condition is presented for the existence of state-feedback $H_2/H_\infty$ optimal controller on the basis of two coupled matrix Riccati equations, which may be solved by a backward iterative algorithm. A numerical example with simulations is supplied to illustrate the proposed theoretical results.  相似文献
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