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The adjacency matrix of a graph is a matrix whose rows and columns are both indexed by vertices of the graph, with a one in the cell for row i and column j when vertices i and j are adjacent, and a zero otherwise. [4] adjacent 1. The relation between two vertices that are both endpoints of the same edge. [2] 2.
Adjacent – next to; Lineal – following along a given path. The shape of the path is not necessarily straight (compare to linear). For instance, a length of rope might be measured in lineal meters or feet. See arc length. Projection / Projected - in architecture, facade sticking out; convex.
The non-adjacent form (NAF) of a number is a unique signed-digit representation, in which non-zero values cannot be adjacent. For example: (0 1 1 1) 2 = 4 + 2 + 1 = 7
Switching {X,Y} in a graph. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs.. Switching a set of vertices in a (simple) graph means reversing the adjacencies of each pair of vertices, one in the set and the other not in the set: thus the edge set is changed so that an adjacent pair becomes nonadjacent and a nonadjacent ...
Let S be an (a,b)-separator, that is, a vertex subset that separates two nonadjacent vertices a and b. Then S is a minimal (a,b)-separator if no proper subset of S separates a and b. More generally, S is called a minimal separator if it is a minimal separator for some pair (a,b) of nonadjacent vertices.
Thus, the relationship between two disjoint modules is either adjacent or nonadjacent. No relationship intermediate between these two extremes can exist. Because of this, modular partitions of where each partition class is a module are of particular interest. Suppose is a modular partition.
In mathematics, in graph theory, the Seidel adjacency matrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex, having 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices.
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).