Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured quantified through uncertainty relations. Although studied since inception theory, problem determining possible expectation values a collection remains, in general, unsolved. By constructing close connection between observ...

In this article, some interesting applications of generalized inverses in the graph theory are revisited. Interesting properties employed to make proof several known results simpler, and techniques such as bordering method inverse complemented matrix methods used obtain simple expressions for Moore-Penrose incidence Laplacian matrix. Some simpler obtained special cases tree graph, complete bipa...

The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula:     ( ) 2 ( ) uv E G u v u v Q Q Q Q GA G , where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of Vphenylenic nanotube ar...

This book is based on Graph Theory courses taught by P.A. Petrosyan, V.V. Mkrtchyan and R.R. Kamalian at Yerevan State University.