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Let A be an edge cut of a connected graph G. Then the cyclic edge connectivity lambda_c(G) is the size of a smallest cyclic edge cut, i.e., a smallest edge cut A such that ...

Let alpha(G) denote the independence number of a graph G. Then the Shannon capacity Theta(G), sometimes also denoted c(G), of G is defined as ...

An example of a subspace of the Euclidean plane that is connected but not pathwise-connected with respect to the relative topology. It is formed by the ray y=0, x<=0 and the ...

The Hadwiger number of a graph G, variously denoted eta(G) (Zelinka 1976, Ivančo 1988) or h(G) (Stiebitz 1990), is the number of vertices in the largest complete minor of G ...

A maximal independent edge set of a graph is an independent edge set that cannot be expanded to another independent edge set by addition of any edge in the graph. Note that a ...

The scramble number sn(G) of a graph G is a graph invariant developed to aid in the study of gonality of graphs. The scramble number is NP-hard to compute (Echavarria et al. ...

The vertex cover number is the size of a minimum vertex cover in a graph G is known as the vertex cover number of G, denoted tau(G). The König-Egeváry theorem states that the ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

The Balaban 11-cage is the unique 11-cage graph, derived via a tree excision from the 12-cage graph by Balaban (1973) and proven unique by McKay and Myrvold in 2003. It is ...

A search algorithm of a graph which explores all nodes adjacent to the current node before moving on. For cyclic graphs, care must be taken to make sure that no nodes are ...