maxdegp

Maxdegp is a term encountered in mathematical and computational literature to describe a degree-related measure that depends on a secondary parameter, p. There is no universally accepted definition, and the exact meaning is highly context-dependent.

One common usage appears in graph theory. Here maxdegp(G, p) is used to denote the maximum vertex degree among a subset of vertices S_p that is defined by a rule involving p. For example, S_p might consist of vertices with degree at least p or vertices selected in a p-threshold process. In this sense maxdegp generalizes the standard maximum degree Δ(G) by restricting attention to a p-dependent portion of the graph.

Another usage arises in algorithm analysis. In parameterized or stepwise algorithms, maxdegp can refer to the largest degree encountered by the algorithm during its execution up to step p, or the maximum degree among elements chosen in the first p iterations. This makes maxdegp a measure that tracks how a graph or structure evolves under a procedure.

Less common is usage in algebraic or combinatorial contexts, where maxdegp may denote the maximum degree of terms under a constraint related to p. Such usage is nonstandard and typically clarified in the surrounding text.

Because the term is not standardized, practitioners should verify the definition from the source. See also degeneracy, degree, maximum degree, and parameterized complexity.