Profile minimization problem for matrices and graphs (Q1327828)

This paper deals with the profile width of a vertex of a simple graph \(G\) and the profile of a numbering \(f\) of \(G\), where the numbering \(f\) of \(G\) is defined as a bijection \(f:V(G) \to \{1,2, \dots, | V(G) |\}\). The authors give the profile of several graphs without proof and succeed in determining a formula for the profile of trees of diameter 4.