Let G be a graph of size n with vertex set V(G) and edge set E(G). A p-labeling of G is a one-to-one function h: V(G) · {0, 1,, 2n} such that{min|h(u)-h(v)|,2n+1-|h(u)-h(v)|}: {u, v} ∈ E(G)} = {1, 2, , n}. Such a labeling of G yields ...
Let G be a simple graph and let us color its edges so that the multisets of colors around each vertex are distinct. The smallest number of colors for which such a coloring exists is called the irregular coloring number of G and is denoted by c(G). We determine the exact value of the...
1) 2-regular graph 2-正则图1. The cordiality of 2-regular graphs is studied and the sufficient and necessary condition for 2-regular graphs G to be cordial is given. 研究2-正则图G的cordial性,证明了2-正则图G是cordial图的充要条件为|G|≠2(mod4);取消了文献[1](Cahit I。
给定一个无向图graph,当这个图为二分图时返回true。 如果我们能将一个图的节点集合分割成两个独立的子集A和B,并使图中的每一条边的两个节点一个来自A集合,一个来自B集合,我们就将这个图称为二分图。 graph将会以邻接表方式给出,graph[i]表示图中与节点i相连的所有节点。每个节点都是一个在0到graph.lengt...
For a graph G, let [Math Processing Error]f2(G) denote the largest number of vertices in a 2-regular subgraph of G. We determine the minimum of [Math Processing Error]f2(G) over 3-regular n-vertex simple graphs G. To do this, we prove that every 3-regular multigraph with exactly ...
Steiner triple system of order 3p in which the leave graph consists of 3 vertex disjoint cycles of length p, then for any 2-factor H with 6+3⩾21p vertices in which all cycles have length divisible by p, there exists a nesting of a partial Steiner triple system with leave graph H....
Let Γ denote a bipartite distance-regular graph with diameter D ⩾ 3 and valency k ⩾ 3. Γ is said to be 2-homogeneous whenever for all integers i(1⩽i⩽D − 1) and for all vertices x,y.z at distance ∂(x, y) = 2, ∂(x, z) = i, ∂(y, z) = i, the ...
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It has been conjectured that every graph of positive size has an ascending subgr... C Makejie - 《高校应用数学学报:英文版(B辑)》 被引量: 18发表: 1998年 正则图连通圈:多种互连网络的统一模型 Cayley图模型,立方体的各种变种(交叉立方体,折叠立方体,M(o)bius立方体等等)以及ILLIAC型互连网络等作为...
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