Let $GP(q,d)$ be the $d$-Paley graph defined on finite field $\mathbb{F}_q$. It is notoriously difficult to improve trivial upper bound $\sqrt{q}$ clique number of $GP(q,d)$. In this paper, we investigate connection between Gauss sums over a and maximum cliques their corresponding generalized Paley graphs. We show that tight if only $d \mid (\sqrt{q}+1)$, which strengthens previous related resu...

A quasi-kernel of a digraph D is an independent set Q⊆V(D) such that for every vertex v∈V(D)﹨Q, there exists directed path with one or two arcs from v to u∈Q. In 1974, Chvátal and Lovász proved has quasi-kernel. 1976, Erdős Székely conjectured sink-free D=(V(D),A(D)) size at most |V(D)|/2. this paper, we give new method show the conjecture holds generalization anti-claw-free digraphs. For any o...

In this work, polynomials and the finite q-exponential operator are constructed. The is used to combine an proof of generating function with its extension, Mehler's formula extension Roger's for . Rogers Al-Salam-Carlitz deduced by giving special values

The complexity of a lattice polynomial is defined inductively, with variables having complexity 0. If p=plv'"vOk or p=plA'''/XOk is the canonical expression of the polynomial O, then the complexity c(p) = l+max{c(p~):l<-i-k}. An n-k lattice inclusion is an inclusion of the form p <-o-with c(p)<-n and c(o-)-k. In this note we use the main result of Day [1] to show that if all the congruence latt...