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The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

Let Y_n denote the graph with vertex set V(X_n), where X_n is the n-hypercube and two vertices are adjacent in Y_n iff they are at distance 1<=d<=2 in X_n. Y_n is not ...

A Lucas cube graph of order n is a graph that can be defined based on the n-Fibonacci cube graph by forbidding vertex strings that have a 1 both in the first and last ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph K_5, and the unique quartic graph on six nodes is the octahedral ...

The wreath graph W(n,k) is the graph obtained by taking n collections of k nodes and arranging around a circle such that all nodes in adjacent collections are connected. ...

The n-Andrásfai graph is a circulant graph on 3n-1 nodes whose indices are given by the integers 1, ..., 3n-1 that are congruent to 1 (mod 3). The Andrásfai graphs have graph ...

The antenna graph is the graph on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["AntennaGraph"].

Given two positive integers n and k, the bipartite Kneser graph H(n,k) is the graph whose two bipartite sets of vertices represent the k-subsets and (n-k)-subsets of ...

The Brinkmann graph (misspelled by Cancela et al. (2004) as "Brinkman") is a weakly regular quartic graph on 21 vertices and 42 edges. It was first mentioned in Brinkmann ...