The atom-bond connectivity (ABC) index of a graph ( , ) G V E is defined as ( ) [ ( ) ( ) 2] / [ ( ) ( )] i j i j i j v v E ABC G d v d v d v d v , where ( ) i d v denotes the degree of the vertex i v of G . This recently introduced molecular structure descriptor found interesting applications in the study of the heats of formation of alkanes. Let ( ) C and ( ) T denote the sets of connected gr...

A natural way for capturing uncertainty in the relational data model is by allowing relations that violate their primary key. A repair of such relation is obtained by selecting a maximal number of tuples without ever selecting two tuples that agree on their primary key. Given a Boolean query q, CERTAINTY(q) is the problem that takes as input a relational database and asks whether q evaluates to...

Let $p=(q^4+q^3+q^2+q+1)/(5,q-1)$ be a prime number, where $q$ is a prime power. In this paper, we will show $Gcong mathrm{PSL}(5,q)$ if and only if $|G|=|mathrm{PSL}(5,q)|$, and $G$ has a conjugacy class size $frac{| mathrm{PSL}(5,q)|}{p}$. Further, the validity of a conjecture of J. G. Thompson is generalized to the groups under consideration by a new way.

In this paper, by integrating the q-rung orthopair fuzzy set (q-ROFS) with N-soft set, we first propose a (q-ROFNSS). Based on q-ROFNSS, explore weighted average (q-ROFNSWA) operator and geometric (q-ROFNSWG) operator, investigate some properties of q-ROFNSWG including idempotency, monotonicity boundedness. Finally, two kinds multiple-attribute group decision-making (MAGDM) methods based aggreg...