The neighbor-scattering number can be computed in polynomial time for interval graphs

TL;DR

This paper proves that the neighbor-scattering number, a measure of graph vulnerability, can be computed efficiently in polynomial time specifically for interval graphs, unlike the NP-complete case for general graphs.

Contribution

The paper establishes a polynomial-time algorithm for calculating the neighbor-scattering number in interval graphs, expanding computational understanding for this graph class.

Findings

Neighbor-scattering number is NP-complete for general graphs.

Explicit formulas exist for some special graphs.

Polynomial-time computation is possible for interval graphs.

Abstract

Neighbor-scattering number is a useful measure for graph vulnerability. For some special kinds of graphs, explicit formulas are given for this number. However, for general graphs it is shown that to compute this number is NP-complete. In this paper, we prove that for interval graphs this number can be computed in polynomial time.