The full wave FDTD method was used to analyze the Hilbert and H fractal curves antennas. The computational results of the input impedance of Hilbert fractal antenna are in good agreement with the experiments in the do...The full wave FDTD method was used to analyze the Hilbert and H fractal curves antennas. The computational results of the input impedance of Hilbert fractal antenna are in good agreement with the experiments in the documents. The results also show that the self-similarity of the fractal structure leads to the multiplicity of resonances over some predetermined operating bandwidths of the antenna. Fractal geometries of Hilbert and H curves can be implemented to miniaturize the antenna, too. The results also show that the higher order fractal antenna leads to the more efficient reduction of the antenna size than the lower order one. Furthermore, the far field patterns remain almost the same as those of the dipole at their own resonant frequencies.展开更多
The total chromatic number xT（G） of a graph G is the minimum number of colors needed to color the elements（vertices and edges） of G such that no adjacent or incident pair of elements receive the same color, G is c...The total chromatic number xT（G） of a graph G is the minimum number of colors needed to color the elements（vertices and edges） of G such that no adjacent or incident pair of elements receive the same color, G is called Type 1 if xT（G） =△（G）＋1. In this paper we prove that the join of a complete bipartite graph Km,n and a cycle Cn is of Type 1.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 deleter...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 （A belong to E（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
Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive intege...Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive integer m and positive integer v, m ≤ v ≤ m + 6.展开更多
Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeic...Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeichel.展开更多
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G)+1/2] for any regular graph G. In this paper, we...The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G)+1/2] for any regular graph G. In this paper, we prove the conjecture for some composition graphs, in particular, for complete multipartite graphs.展开更多
文摘The full wave FDTD method was used to analyze the Hilbert and H fractal curves antennas. The computational results of the input impedance of Hilbert fractal antenna are in good agreement with the experiments in the documents. The results also show that the self-similarity of the fractal structure leads to the multiplicity of resonances over some predetermined operating bandwidths of the antenna. Fractal geometries of Hilbert and H curves can be implemented to miniaturize the antenna, too. The results also show that the higher order fractal antenna leads to the more efficient reduction of the antenna size than the lower order one. Furthermore, the far field patterns remain almost the same as those of the dipole at their own resonant frequencies.
文摘The total chromatic number xT（G） of a graph G is the minimum number of colors needed to color the elements（vertices and edges） of G such that no adjacent or incident pair of elements receive the same color, G is called Type 1 if xT（G） =△（G）＋1. In this paper we prove that the join of a complete bipartite graph Km,n and a cycle Cn is of Type 1.
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 （A belong to E（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.
文摘Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive integer m and positive integer v, m ≤ v ≤ m + 6.
基金Supported partially by Project 02139 of Ministry of Education, China
文摘Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeichel.
基金This work is partially supported by National Natural Science foundation of China Doctoral foundation of the Education Committee of China.
文摘The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G)+1/2] for any regular graph G. In this paper, we prove the conjecture for some composition graphs, in particular, for complete multipartite graphs.
