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In graph theory, a branch of mathematics and computer science, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find a shortest closed path or circuit that visits every edge of an (connected) undirected graph at least once. When the graph has an Eulerian circuit (a closed walk that covers every ...
Neighbourhood (graph theory) In this graph, the vertices adjacent to 5 are 1, 2 and 4. The neighbourhood of 5 is the graph consisting of the vertices 1, 2, 4 and the edge connecting 1 and 2. For other meanings of neighbourhoods in mathematics, see Neighbourhood (mathematics). In graph theory, an adjacent vertex of a vertex v in a graph is a ...
Graph. [] A graph with three vertices and three edges. In one restricted but very common sense of the term, [ 1 ][ 2 ] a graph is an ordered pair comprising: V {\displaystyle V} , a set of vertices (also called nodes or points); E ⊆ {{x, y} ∣ x, y ∈ V and x ≠ y} {\displaystyle E\subseteq \ {\ {x,y\}\mid x,y\in V\; {\textrm {and}}\;x\neq ...
v − 1. Chromatic number. 2 if v > 1. Table of graphs and parameters. In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently ...
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge– vertex connectivity. Formally, an automorphism of a graph G = (V, E) is a permutation σ of the vertex set V, such that the pair of vertices (u, v) form an edge if and only if the pair ...
Its negative resolution by Leonhard Euler, in 1736, [1] laid the foundations of graph theory and prefigured the idea of topology. [ 2 ] The city of Königsberg in Prussia (now Kaliningrad , Russia ) was set on both sides of the Pregel River , and included two large islands— Kneiphof and Lomse —which were connected to each other, and to the ...
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2. Feedback vertex set [2][3]: GT7. Feedback arc set [2][3]: GT8.
Shortest path problem. Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. [1]
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