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A chordless graph is a simple graph possessing no chords. A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which ...

The assignment of labels or colors to the edges or vertices of a graph. The most common types of graph colorings are edge coloring and vertex coloring.

An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

As defined in this work, a wheel graph W_n of order n, sometimes simply called an n-wheel (Harary 1994, p. 46; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 78), is a ...

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 (P,B) denote a configuration with v points P={p_1,...,p_v} and b lines ("blocks") B=(B_1,...,B_b). Then the Levi graph L(P,B), also called the incidence graph, of a ...

The graph product denoted G-H and defined by the adjacency relations (gadjg^') or (g=g^' and hadjh^'). The graph lexicographic product is also known as the graph composition ...

A graceful graph is a graph that can be gracefully labeled. Special cases of graceful graphs include the utility graph K_(2,3) (Gardner 1983) and Petersen graph. A graph that ...

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...