The metric dimension problem was first introduced in 1975 by Slater [35], and independently by Harary and Melter [16] in 1976; however the problem for hypercube was studied (and solved asymptotically) much earlier in 1963 by Erdős and Rényi [10]. A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of...

Trust has been found to be important for integrating suppliers ́ knowledge in new product development (NPD). Different degrees of trust have different consequences for NPD. This paper investigates the effects of trust for capturing supplier knowledge in NPD in different situations. Two different NPD collaborations, identified as polar cases, are studied. The findings indicate differences in know...

[This article examines whether trust or fiduciary law provides potential ‘stolen wages’ plaintiffs with a strong basis for a claim over money in bank accounts that previous governments held on the plaintiffs’ behalf. It also considers the broader issue of whether governments owed a fiduciary duty flowing from their obligations under general ‘protective’ legislation to prevent such workers from ...

Rosenbloom and Tsfasman introduced a new metric (RT metric) which is a generalization of the Hamming metric. In this paper we study the distance graphs of spaces Zn q and Sn with Rosenbloom -Tsfasman metric. We also describe the degrees of vertices, components and the chromatic number of these graphs. Distance graphs of general direct product spaces also described.

A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with inner product 〈·, ·〉 : X ×X → K satisfying • 〈x + y, z〉 = 〈x, z〉+〈y, z〉, • 〈αx, y〉 =α〈x, y〉, • 〈x, y〉 = 〈y, x〉, • 〈x, x〉 ≥ 0 with 〈x, x〉 = 0 ⇐⇒ x = 0. [2] An inner product induces a norm on X via ‖x‖ =p...