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A vertex-induced subgraph (sometimes simply called an "induced subgraph") is a subset of the vertices of a graph G together with any edges whose endpoints are both in this ...

A forest is an acyclic graph (i.e., a graph without any graph cycles). Forests therefore consist only of (possibly disconnected) trees, hence the name "forest." Examples of ...

The arithmetic-geometric energy of a graph is defined as the graph energy of its arithmetic-geometric matrix, i.e., the sum of the absolute values of the eigenvalues of its ...

The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed. Similarly, the circumradius of a polyhedron is the radius of a ...

A quasiregular polyhedron is the solid region interior to two dual regular polyhedra with Schläfli symbols {p,q} and {q,p}. Quasiregular polyhedra are denoted using a ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

An articulation vertex of a connected graph, also called a cut-vertex (Harary 1994, p. 26; West 2000; Gross and Yellen 2006) or "cutpoint" (Harary 1994, p. 26), is a vertex ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...