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A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of ...

The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its ...

Let gamma(G) denote the domination number of a simple graph G. Then Vizing (1963) conjectured that gamma(G)gamma(H)<=gamma(G×H), where G×H is the graph product. While the ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

The Pappus configuration is the 9_3 configuration illustrated above that appears in Pappus's hexagon theorem. It is one of the three 9_3 configurations. The Levi graph of the ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...

There are four strongly regular graphs with parameters (nu,k,lambda,mu)=(28,12,6,4), one of them being the triangular graph of order 8. The other three such graphs are known ...

A graph with minimum vertex degree at least 5 is a line graph iff it does not contain any of the above six graphs, known in this work as Metelsky graphs, as an induced ...

A chord of a graph cycle C is an edge not in the edge set of C whose endpoints lie in the vertex set C (West 2000, p. 225). For example, in the diamond graph as labeled ...

A chordless cycle of a graph G is a graph cycle in G that has no cycle chord. Unfortunately, there are conflicting conventions on whether or not 3-cycles should be considered ...