ON $(d,2)$-DOMINATING NUMBERS OF BUTTERFLY NETWORKS$^{*\dagger}$

Incidence dominating numbers of graphs

In this paper, the concept of incidence domination number of graphs  is introduced and the incidence dominating set and  the incidence domination number  of some particular graphs such as  paths, cycles, wheels, complete graphs and stars are studied.

Rabin numbers of Butterfly networks

Reliability and efficiency are important criteria in the design of interconnection networks. Recently, the w-wide diameter d,(G), the (W 1 )-fault diameter D,,(G), and the w-Rabin number r,(G) have been used to measure network reliability and efficiency. In this paper, we study these parameters for an important class of parallel networks Butterfly networks. The main result of this paper is to d...

Trees with extremal numbers of dominating sets

Hadwiger numbers and over-dominating colourings

Motivated by Hadwiger’s conjecture, we say that a colouring of a graph is over-dominating if every vertex is joined to a vertex of each other colour and if, for each pair of colour classes C1 and C2, either C1 has a vertex adjacent to all vertices in C2 or C2 has a vertex adjacent to all vertices in C1. We show that a graph that has an over-dominating colouring with k colours has a complete min...

Quantum Reality, Complex Numbers and the Meteorological Butterfly Effect

Meteorology is a wonderfully interdisciplinary subject. But can nonlinear thinking about predictability of weather and climate contribute usefully to issues in fundamental physics? Although this might seem extremely unlikely at first sight, an attempt is made to answer the question positively. The long-standing conceptual problems of quantum theory are outlined, focussing on indeterminacy and n...