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Let G be a finite graph and v a vertex of G. The stabilizer of v, stab(v), is the set of group elements {g in Aut(G)|g(v)=v}, where Aut(g) is the graph automorphism group. ...

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 ...

Let G be a simple connected graph, and take 0<=i<=d(G), where d(G) is the graph diameter. Then G has global parameters c_i (respectively a_i, b_i) if the number of vertices ...

A cograph (or "complement-reducible graph") is simple graph defined by the criteria 1. K_1 is a cograph, 2. If X is a cograph, then so is its graph complement, and 3. If X ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

Graph Strength

The Balaban 10-cage is one of the three (3,10)-cage graphs (Read and Wilson 1998, p. 272). The Balaban (3,10)-cage was the first known example of a 10-cage (Balaban 1973, ...

The Sombor spectral radius rho_(Sombor) of a graph is defined as the largest eigenvalue of the Sombor matrix. Liu et al. (2022) shows that for any tree, ...

In a graph G, two graph vertices are adjacent if they are joined by a graph edge.

A graph vertex in a graph is said to be an even node if its vertex degree is even.