The concept of inverse domination was introduced by Kulli V.R. and Sigarakanti S.C. [9] . Let D be a  set of G. A dominating set D1  VD is called an inverse dominating set of G with respect to D. The inverse domination number   (G) is the order of a smallest inverse dominating set. Motivated by this definition we define another parameter as follows. Let D be a maximum independent set in G. ...

If A(z) is a function of a real or complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A(z) g-Drazin invertible, we study conditions under which the g-Drazin inverse AD(z) is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a matrix valued function and a result on diff...

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Aim of this article is to find the maximum and minimum solution of the fuzzy neutrosophic soft relational equations xA=b and Ax=b, where x and b are fuzzy neutrosophic soft vector and A is a fuzzy neutrosophic soft matrix. Wheneve...

We present new conditions under which Cline?s formula and Jacobson?s lemma for g-Drazin inverse hold. Let A be a Banach algebra, let a,b ? satisfying akbkak = ak+1 some k N. prove that has if only bkak inverse. In this case, (bkak)d bk(ad)2ak ad ak[(bkak)d]k+1. Further, we study in algebra the preceding condition. The common spectral property of bounded linear operators on space is thereby obta...

Message passing on a factor graph is powerful paradigm for the coding of approximate inference algorithms arbitrarily large graphical models. The notion fragment allows compartmentalisation algebra and computer code. We show that Inverse G-Wishart family distributions enables fundamental variational message fragments to be expressed elegantly succinctly. Such arise in models which concerning co...

We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup S and a homomorphism φ of S onto a group G, we show, under an assumption on ker(φ), that S has weak containment if and only if G is amenable and ker(φ) has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show tha...

Let G = (V, E) be a graph. Let D be a minimum secure total dominating set of G. If V – D contains a secure total dominating set D' of G, then D' is called an inverse secure total dominating set with respect to D. The inverse secure total domination number γst(G) of G is the minimum cardinality of an inverse secure total dominating set of G. The disjoint secure total domination number γstγst(G) ...