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Finding all vertices adjacent to a given vertex in an adjacency list is as simple as reading the list, and takes time proportional to the number of neighbors. With an adjacency matrix, an entire row must instead be scanned, which takes a larger amount of time, proportional to the number of vertices in the whole graph.
In graph theory, a clique (/ ˈ k l iː k / or / ˈ k l ɪ k /) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph is an induced subgraph of that is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical ...
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
Synonym for non-edge, a pair of non-adjacent vertices. anti-triangle A three-vertex independent set, the complement of a triangle. apex 1. An apex graph is a graph in which one vertex can be removed, leaving a planar subgraph. The removed vertex is called the apex. A k-apex graph is a graph that can be made planar by the removal of k vertices. 2.
Every tree has a center consisting of one vertex or two adjacent vertices. The center is the middle vertex or middle two vertices in every longest path. Similarly, every n-vertex tree has a centroid consisting of one vertex or two adjacent vertices. In the first case removal of the vertex splits the tree into subtrees of fewer than n/2
Finding all vertices adjacent to a given vertex in an adjacency list is as simple as reading the list. With an adjacency matrix, an entire row must instead be scanned, which takes O (| V |) time. Whether there is an edge between two given vertices can be determined at once with an adjacency matrix, while requiring time proportional to the ...
every two adjacent vertices have λ common neighbours, and; every two non-adjacent vertices have μ common neighbours. Such a strongly regular graph is denoted by srg(v, k, λ, μ); its "parameters" are the numbers in (v, k, λ, μ). Its complement graph is also strongly regular: it is an srg(v, v − k − 1, v − 2 − 2k + μ, v − 2k + λ).