let $gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. denote by $upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. in the classes of graphs $gamma_{n,kappa}$ and $upsilon_{n,beta}$, the elements having maximum augmented zagreb index are determined.

it is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (castelnuovo-mumford) regularity. as a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph g are equal provided g is well-covered bipa...

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...

language is a system and every system has rules that govern the structure of its vocabulary. the rules of the arabic language are based on the vowels that consistent with the meanings used in the context represent the words' position. there are some basic rules in addition to vowels which are mostly seen in the written texts. one of these rules is the matching rule that refers to the condi...

Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...