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Robertson's apex graph is the 15-vertex graph illustrated above constructed by Neil Robertson as an example of an apex graph that is not YDeltaY-reducible. The graph may be ...

A connected graph having e graph edges is said to be sequential if it is possible to label the nodes i with distinct integers f_i in {0,1,2,...,e-1} such that when graph edge ...

Let a simple graph G have n vertices, chromatic polynomial P(x), and chromatic number chi. Then P(G) can be written as P(G)=sum_(i=0)^ha_i·(x)_(p-i), where h=n-chi and (x)_k ...

In algebraic topology, a p-skeleton is a simplicial subcomplex of K that is the collection of all simplices of K of dimension at most p, denoted K^((p)). The graph obtained ...

Consider a star graph S_(n+1) consisting of a central hub vertex and n spokes, but instead of placing a single point at the end of each spoke, place k points along it (in ...

The stacked book graph of order (m,n) is defined as the graph Cartesian product S_(m+1) square P_n, where S_m is a star graph and P_n is the path graph on n nodes. It is ...

A Steiner system S(t,k,v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. ...

A subgraph G^' of a graph G is a graph G^' whose vertex set and edge set are subsets of those of G. If G^' is a subgraph of G, then G is said to be a supergraph of G^' ...

For a graph vertex x of a graph, let Gamma_x and Delta_x denote the subgraphs of Gamma-x induced by the graph vertices adjacent to and nonadjacent to x, respectively. The ...

A graph that can be reduced to another graph with the same degree sequence by edge-switching is known as a switchable graph. Conversely, a graph that cannot be reduced to ...