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...

Graph theory is a well-established mathematical concept that widely used in numerous applications such as biology, chemistry and network analysis. The advancement the of graph has led to development called autocatalytic set. In this paper, modeling technique namely graph-based dynamic palm oil refining process introduced. system parameters are identified detail beginning paper. involved chemica...

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

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

Graphs may be classified in many ways apart from their order. A complete graph has each distinct pair of vertices connected by an edge. Many interesting problems arise in looking at complete graphs, several of which have to do with determining whether or not it is possible to pass through every vertex and edge once and only once (a Peterson cycle). A connected graph allows movement from any ver...

Course number: 0366.3267. When and where: Wednesdays 15-18, Ornstein 111. Prospective audience: the course is intended for second and third year undergraduate students in Mathematics or Computer Science. Prerequisites: first year courses in mathematics, most notably Discrete Mathematics or Introduction to Combinatorics. Requirements and grade: Homeworks will be given once every two-three weeks;...

These notes have not been checked by Prof. A.G. Thomason and should not be regarded as ocial notes for the course. In particular, the responsibility for any errors is mine please email Sebastian Pancratz (sfp25) with any comments or corrections.