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A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

Bonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either ...

The adjacency matrix, sometimes also called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

The Harary index of a graph G on n vertices was defined by Plavšić et al. (1993) as H(G)=1/2sum_(i=1)^nsum_(j=1)^n(RD)_(ij), (1) where (RD)_(ij)={D_(ij)^(-1) if i!=j; 0 if ...

The mathematical study of the properties of the formal mathematical structures called graphs.

The multiplicity of a multigraph is its maximum edge multiplicity.

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...