In this paper, we consider the problem of reducing semitotal domination number a given graph by contracting k edges, for some fixed k≥1. We show that can always be done with at most 3 edge contractions and further characterise those graphs requiring 1, 2 or contractions, respectively, to decrease their number. then study complexity k=1 obtain in particular complete dichotomy monogenic classes.

Response spectral matching is a process in which a real recorded earthquake ground motion is modified such that its response spectrum matches a desired target spectrum across a range of periods. Spectral matching algorithms aim to minimise artificial adjustments introduced to the seed, such that original non-stationary characteristics, such as velocity pulses commonly observed in ground motions...

a emph{signed graph} (or, in short, emph{sigraph}) $s=(s^u,sigma)$ consists of an underlying graph $s^u :=g=(v,e)$ and a function $sigma:e(s^u)longrightarrow {+,-}$, called the signature of $s$. a emph{marking} of $s$ is a function $mu:v(s)longrightarrow {+,-}$. the emph{canonical marking} of a signed graph $s$, denoted $mu_sigma$, is given as $$mu_sigma(v) := prod_{vwin e(s)}sigma(vw).$$the li...