Tree Graphs and Orthogonal Spanning Tree Decompositions

Given a graph G, we construct T(G), called the tree graph of G. The vertices of T(G) are the spanning trees of G, with edges between vertices when their respective spanning trees differ only by a single edge. In this paper we detail many new results concerning tree graphs, involving topics such as clique decomposition, planarity, and automorphism groups. We also investigate and present a number of new results on orthogonal tree decompositions of complete graphs

Effect of mineral matter on the reactivity of coke and its replication in a coke analogue

The reactivity of coke analogues doped with minerals to mimic the mineralogy of specific industrial cokes was compared with the reactivity of the industrial cokes. The reactivity was assessed in a pseudo-CRI type test. This involved reacting the carbonaceous materials (analogue and industrial coke) in CO₂ at 1 100°C in a thermos-gravimetric system. In this comparison, the mineral matter added to the coke analogue was prepared from ashing of the industrial cokes. A distinct ranking of reactivity for the industrial cokes was determined to be coke A < coke B < coke C. The high reactivity of coke C was attributed to the high iron content in its ash. The higher reactivity of coke B over coke A was attributed to its higher porosity and lower rank (of the original coal carbon type) of the industrial cokes. The coke analogue replicated the increased reactivity of coke C over cokes A and B, indicating that the coke analogue is able to some extent to replicate the effect of coke mineralogy on coke reactivity in CO₂. The use of the coke analogue allowed assessment of the difference in the reactivities of cokes A and B. When porosity and carbon type were fixed by use of the analogue, the reactivities of the analogues of cokes A and B were found to be similar