  We equip the edges of a deterministic graph $H$ with independent but not
necessarily identically distributed weights and study a generalized version of
matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property
that end-vertices of any two distinct edges are at least a minimum distance
apart. We call such matchings as strong matchings and determine bounds on the
expectation and variance of the minimum weight of a maximum strong matching.
Next, we consider an inhomogenous random graph whose edge probabilities are not
necessarily the same and determine bounds on the maximum size of a strong
matching in terms of the averaged edge probability. We use local vertex
neighbourhoods, the martingale difference method and iterative exploration
techniques to obtain our desired estimates.
