A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd（vi） = Σ（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,..., ｜V（G）｜, where d（vi） denotes the d...A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd（vi） = Σ（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,..., ｜V（G）｜, where d（vi） denotes the degree of vertex vi. Let ni denote the number of vertices with degree i. This paper deals with the 3-Hgraphs and determines their degree series. Moreover, the 3-Hgraphs with bounded ni （1 ≤ i ≤ 7） are studied and some interesting results are obtained.展开更多
A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd（ui） = ∑（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,…, ｜V（G）｜, where d（vi） denotes the degr...A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd（ui） = ∑（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,…, ｜V（G）｜, where d（vi） denotes the degree of vertex vi. In this paper, some harmonic properties of the complement and line graph are given, and some algebraic properties for the λ-Hgraphs are obtained.展开更多
基金supported by the National Natural Science Foundation of China (10771080)the Specialized Research Fund for the Doctoral Program of Higher Eduction (20070574006)
文摘A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd（vi） = Σ（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,..., ｜V（G）｜, where d（vi） denotes the degree of vertex vi. Let ni denote the number of vertices with degree i. This paper deals with the 3-Hgraphs and determines their degree series. Moreover, the 3-Hgraphs with bounded ni （1 ≤ i ≤ 7） are studied and some interesting results are obtained.
基金supported by the fund of South China Agricultural University (4900-K08225)supported by the National Natural Science Foundation of China(10771080)Specialized Research Fund for the Doctoral Program of Higher Eduction (20070574006)
文摘A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd（ui） = ∑（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,…, ｜V（G）｜, where d（vi） denotes the degree of vertex vi. In this paper, some harmonic properties of the complement and line graph are given, and some algebraic properties for the λ-Hgraphs are obtained.
