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This undirected cyclic graph can be described by the three unordered lists {b, c}, {a, c}, {a, b}. In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph.
A line perfect graph. The edges in each biconnected component are colored black if the component is bipartite, blue if the component is a tetrahedron, and red if the component is a book of triangles. The line graph of the complete graph K n is also known as the triangular graph, the Johnson graph J(n, 2), or the complement of the Kneser graph ...
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.
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 three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A proper AVD-total-coloring of the complete graph K 4 with 5 colors, the minimum number possible. In graph theory, a total coloring is a coloring on the vertices and edges of a graph such that: (1). no adjacent vertices have the same color; (2). no adjacent edges have the same color; and (3). no edge and its endvertices are assigned the same color.
The edge boundary is the set of edges with one endpoint in the inner boundary and one endpoint in the outer boundary. [1] These boundaries and their sizes are particularly relevant for isoperimetric problems in graphs, separator theorems, minimum cuts, expander graphs, and percolation theory.
Two orientations are shown as adjacent when they differ in the direction of a single edge. In graph theory, an acyclic orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that does not form any directed cycle and therefore makes it into a directed acyclic graph. Every graph has an acyclic orientation.