Lower bounds for some decision problems over C

Lower bounds on the signed (total) $k$-domination number

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...

Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

Lower Bounds for Query Complexity of Some Graph and Matrix Problems

The paper [4] by H.Buhrman and R. de Wolf contains an impressive survey of solved and open problems in quantum query complexity, including many graph problems. We use recent results by A.Ambainis [1] to prove higher lower bounds for some of these problems. Some of our new lower bounds do not close the gap between the best upper and lower bounds. We prove in these cases that it is impossible to ...

Some Lower Bounds for Estrada Index

On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...