Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain var...

The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values for the vertex-deleted subgraphs of the same graph. This note discusses the polynomial reconstructibility of the matching polynomial. We collect previous resul...

The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G. We define the matching energy (ME) of the graph G as the sum of the absolute values of the zeros of the matching polynomial of G, and determine its basic properties. It is pointed out that the chemical applications of ME go back to the 1970s.

The concept of the matching polynomial of a graph, introduced by Farrell in 1979, has received considerable attention and research. In this paper, we generalize this concept and introduce the matching polynomial of hypergraphs. A recurrence relation of the matching polynomial of a hypergraph is obtained. The exact matching polynomials of some special hypergraphs are given. Further, we discuss t...

this paper presents the application of the matching pursuit method to model synchronous generator. this method is useful for online analysis. in the proposed method, the field voltage is considered as input signal, while the terminal voltage and active power of the generator are output signals. usually, the difference equation with a second degree polynomial structure is used to estimate the co...

In this paper we study various extremal problems related to some combinatorially defined graph polynomials such as matching polynomial, chromatic polynomial, Laplacian polynomial. It will turn out that many problems attain its extremal value in the class of threshold graphs. To attack these kinds of problems we survey several applications of the so-called Kelmans transformation. Mea culpa. This...