Let $G$ be a $(p,q)$ graph. Let $f:V(G)to{1,2, ldots, k}$ be a map where $k in mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $gcd(f(u),f(v))$. $f$ is called $k$-Total prime cordial labeling of $G$ if $left|t_{f}(i)-t_{f}(j)right|leq 1$, $i,j in {1,2, cdots,k}$ where $t_{f}(x)$ denotes the total number of vertices and the edges labelled with $x$. A graph with a $k$-total prime cordi...

Let k ≥ 1 be an integer, and let G be a finite and simple graph with vertex set V (G). A signed total Italian k-dominating function (STIkDF) on a graph G is a functionf : V (G) → {−1, 1, 2} satisfying the conditions that $sum_{xin N(v)}f(x)ge k$ for each vertex v ∈ V (G), where N(v) is the neighborhood of $v$, and each vertex u with f(u)=-1 is adjacent to a vertex v with f(v)=2 or to two vertic...

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Let $(X,d)$ be a compactmetric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all  continuous complex-valued functions $f$ on$X$ for which$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}

In this paper, we investigate cyclic code over the ring Fpk + vFpk + v 2 Fpk + ...+ v r Fpk , where v = v, p a prime number, r > 1 and gcd(r, p) = 1, we prove as generalisation of [9] that these codes are principally generated, give generator polynomial and idempotent depending on idempotents over this ring as response to an open problem related in [11]. we also give a gray map and proprieties ...