Some Combinatorial Problems in Power-Law Graphs

The power-law behavior is ubiquitous in a majority of real-world networks, and it was shown to have strong effect on various combinatorial, structural, dynamical properties graphs. For example, has been that real-life both the matching number domination are relatively smaller, compared with homogeneous In this paper, we study analytically several combinatorial problems for two graphs same vertices, edges, power exponent. graphs, determine exactly or recursively their number, independence maximum matchings, independent sets, minimum dominating sets. We show itself cannot characterize heterogenous graph. Since studied here found wide applications different fields, such as structural controllability complex our work offers insight these