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Graph Strength

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. The most common type of vertex ...

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

An Eulerian graph is a graph containing an Eulerian cycle. The numbers of Eulerian graphs with n=1, 2, ... nodes are 1, 1, 2, 3, 7, 15, 52, 236, ... (OEIS A133736), the first ...

An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

The study of how the intrinsic structure of graphs ensures certain types of properties (e.g., clique-formation and graph colorings) under appropriate conditions.

The Markström graph is a cubic planar graph on 24 vertices which lacks cycles of length 4 and 8 but contains cycles of length 16. (In particular, it contains cycles of ...

The Randić spectral radius rho_(Randic) of a graph is defined as the largest eigenvalue of its Randić matrix.

The second Zagreb index for a graph with vertex count n and vertex degrees d_i for i=1, ..., n is defined by Z_2=sum_((i,j) in E(G))d_id_j, where E(G) is the edge set of G.

For a graph G and a subset S of the vertex set V(G), denote by N_G[S] the set of vertices in G which are in S or adjacent to a vertex in S. If N_G[S]=V(G), then S is said to ...