独立集中具有最小特定度和的点的上可嵌入图类(英)

结合边连通度，探讨了独立集中具有最小特定度和的点的上可嵌入图.得到了下列结果. (1)设G,是一个2-边连通简单图且满足条件:对任意一个G的3-独立集I, ∨x_i ,x_j ∈I (i,j = 1,2,3), d(x_i ,x_j)≧3 (1 ≦ i ≠ j ≦ 3) =>∑_{i = 1}³ d(x_i) ≧ v + 1(v = | V(G)|}), 则G是上可嵌入的;(2)设G是一个3-边连通简单图且满足条件:对任意一个G的6-独立集I, ∨x_i ,x_j ∈I (1≦i,j≦6), d(x_i,x_j) ≧3(1 ≦ i ≠ j ≦ 6) => ∑_{i = 1}⁶ d(x_i) ≧ v + 1(v = | V(G)|), 则G是上可嵌入的.

Classes of Upper Embeddable Graphs with Specific Minimum Degree-Sum of Vertices in Independent-Set(English)

Combined with the edge-connectivity, this paper investigated the upper embeddable graphs with specific minimum degree-sum of vertices in its independent-set, and obtained the following results. (1) Let G be a 2-edge-connected simple graph, if G satisfies the following conditions: for any 3-independent set I in G, (A)xi,xj ∈ I (i,j = 1,2,3), d(xi,xj) ≥ 3 (1 ≤ i ≠j ≤ 3) (=) 3∑i=1d(xi) ≥v+1(v=|V(G)|), then G is upper embeddable; (2) Let G be a 3-edgeconnected simple graph, if G satisfies the following conditions: for any 6-independent set I in G,(A)xi,xj ∈ I(1 ≤i,j ≤6), d(xi,xj) ≥3(1 ≤i≠j ≤6) (=)3 ∑i=1d(xi) ≥v+1 (v=|V(G)|),then G is upper embeddable.