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The neighborhood complex N(G) of a locally finite graph G is defined as the abstract simplicial complex formed by the subsets of the neighborhoods of all vertices of G.

An ordered pair representation is a representation of a directed graph in which edges are specified as ordered pairs or vertex indices. The ordered pairs representation of a ...

The graph complement of a perfect graph is itself perfect. Originally known as the weak perfect graph conjecture (Fulkerson 1971), the result was subsequently proved by ...

The so-called reaching algorithm can solve the shortest path problem (i.e., the problem of finding the graph geodesic between two given nodes) on an m-edge graph in O(m) ...

The shortest path problem seeks to find the shortest path (a.k.a. graph geodesic) connecting two specific vertices (u,v) of a directed or undirected graph. The length of the ...

Tutte's wheel theorem states that every polyhedral graph can be derived from a wheel graph via repeated graph contraction and edge splitting. For example, the figure above ...

An s-route of a graph G is a sequence of vertices (v_0,v_1,...,v_s) of G such that v_iv_(i+1) in E(G) for i=0, 1, ..., s-1 (where E(G) is the edge set of G) and ...

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the P-anticomplementary conjugate of U is the point where h(a,b,c,p,q,r,u,v,w) ...

A ruled surface M is a normal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vN^^(u), where N is the normal vector (Gray 1993, pp. 352-354; first edition ...

If a map f:G->G^' from a group G to a group G^' satisfies f(ab)=f(b)f(a) for all a,b in G, then f is said to be an antihomomorphism. Moreover, if G and G^' are isomorphic, ...