We enumerate by computer algorithms all simple t (t +7, t +1, 2) designs for 1 t 5, i.e. for all possible t , and this enumeration is new for t 3. The number of nonisomorphic designs is equal to 3, 13, 27, 1 and 1 for t = 1, 2, 3, 4 and 5, respectively. We also present some properties of these designs including orders of their full automorphism groups and resolvability.

Graphs of order n with fault-tolerant metric dimension have recently been characterized.This paper points out an error in the proof this characterization. We show that complete multipartite graphs also n, which provides infinite family counterexamples to Furthermore, we find exact values metric, edge mixed-metric dimensions, domination number, locating-dominating and metric-locating-dominating ...

A vertex w ∈ V H distinguishes (or resolves) two elements (edges or vertices) id="M2"> a , z ∪ E if id="M3"> d ≠ . set id="M4"> W m </msu...

In this work we study the problem of secure communication over a fully quantum Gel’fand-Pinsker channel. The best known achievability rate for this channel model in the classical case was proven by Goldfeld, Cuff and Permuter in [1]. We generalize the result of [1]. One key feature of the results obtained in this work is that all the bounds obtained are in terms of error exponent. We obtain our...