图是用来体现对象之间联系的一种数据结构,它由顶点(vertices)和边(edges) 例如下面的图所示,顶点由圆圈表示,边由连接两个顶点的直线表示。 Graph1.png 有权图 在有权图中,每一条边都有一个权重。 在航空业,设想一下以下飞行路线: Graph2.png 在这个示例中,图的顶点代表一个国家或者一个城市,边代表从一个...
一个自环(loop)是一条端点为同一个点的边,多重边(multiple edges)为有同一对端点的边,如下图 一个简单图(simple graph)是没有自环和多重边的图。 两个图 G,H 是相同的(identical)若V(G)=V(H) 且E(G)=E(H)。 但是对于图来说,即使不是相同的图(比如节点的顺序不同),也仍然可能是同一个样子的...
A graph has strong convex dimension 2 if it admits a straight-line drawing in the plane such that its vertices form a convex set and the midpoints of its edges also constitute a convex set. Halman, Onn, and Rothblum conjectured that graphs of strong convex dimension 2 are planar and ...
In turn, both of these results generalize Dirac's classical result on the existence of simplicial vertices in chordal graphs. We prove that every graph with an edge has an avoidable edge, which settles the first open case of the conjecture. We point out a close relationship between avoidable ...
Edge random graphs are Erdos-Renyi random graphs, vertex random graphs are generalizations of geometric random graphs, and vertex-edge random graphs generalize both. The names of these three types of random graphs describe where the randomness in the models lies: in the edges, in the vertices, ...
The majority of graph theory research on parameters involved with domination, independence, and irredundance has focused on either sets of vertices or sets of edges; for example, sets of vertices that dominate all other vertices or sets of edges that dominate all other edges. There has been ver...
两个或多个有相同端点的连接被称为平行边(parallel edges)。在图1.1的图G中,边b就是一个环,其他所有的边都是连接;边d和f是平行边。 在本书中,大写字母G表示一个图,此外,在不引起歧义的情况下,我们在讨论过程中省略字母G,例如用V和E而不是V(G)和E(G)来表示顶点与边的集合。在这种情况下,我们用n和...
A graph is a collection ofnodesandedgesthat represents relationships: Nodesare vertices that correspond to objects. Edgesare the connections between objects. The graph edges sometimes haveWeights, which indicate the strength (or some other attribute) of each connection between the nodes. ...
Let H be the graph consisting of the vertices and edges used on this trail. Delete the edges in H from G. From the reasoning in the first part of the proof, this wil change the degree of each vertex by an even amount, so the resulting graph G^\prime has all vertices with even ...
The vertexedge degree of the vertex v, deG(v), equals to the number of different edges that are incident to any vertex from the open neighborhood of v. Also, the edge-vertex degree of the edge e = uv, dvG(e), equals to the number of vertices of the union of the open neighborhood...