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A k-dispersed labelling of a graph G on n vertices is a labelling of the vertices of G by the integers 1,...,n such that d(i,i+1) ≥ k for 1 ≤ i ≤ n − 1. Here DL(G) denotes the maximum value of k such that G has a k-dispersed labelling. In this paper, we study upper and lower bounds on DL(G). Computing DL(G) is NP-hard. However, we determine the exact value of DL(G) for cycles, paths, grids, hypercubes and complete binary trees. We also give a product construction and we prove a degree-based bound. 

Using a key result of Mancinska and Roberson characterizing quantum isomorphism in terms of planar homomorphism counts and using the theory of scaffolds, the authors construct large families of graphs that are pairwise non-isomorphic yet quantum isomorphic. All examples so far arise from Hadamard matrices. 

This paper introduces a generalization of perfect state transfer in continuous time quantum walks on graph and explores basic properties and example of this phenomenon. 

The North American Electric Reliability Corporation (NERC) tracks the restoration of the North American transmission system after events which test the grid resilience and reliability. Quantifying and analyzing these historical events is a foundation for studying and maintaining resilience. After showing that the largest recent events are dominated by extreme weather events, the paper analyzes these events by extracting the restore process for each event and defining, calculating, and discussing various metrics that quantify the restoration. The metrics include a duration metric of time to substantial restoration. In 2021, Hurricane Ida was the largest resilience event in the North American system. A case study of Hurricane Ida analyzes the generator outages and restoration as well as the transmission system outages and restoration. 

The current study reports AxA’1-xByB’1-yO3-𝛿 perovskite redox catalysts (RCs) for CO2-splitting and methane partial oxidation (POx) in a cyclic redox scheme. Strontium (Sr) and iron (Fe) were chosen as A and B site elements with A’ being lanthanum (La), samarium (Sm) or yttrium (Y), and B’ being manganese (Mn), or titanium (Ti) to tailor their equilibrium oxygen partial pressures (P_(O_2 ) s) for CO2-splitting and methane partial oxidation. DFT calculations were performed for predictive optimization of the oxide materials whereas experimental investigation confirmed the DFT predicted redox performance. The redox kinetics of the RCs improved significantly by 1 wt.% ruthenium (Ru) impregnation without affecting their redox thermodynamics. Ru impregnated LaFe0.375Mn0.625O3 (A=0, A’=La, B=Fe, and B’=Mn) was the most promising RC in terms of its superior redox performance (CH4/CO2 conversion >90% and CO selectivity~ 95%) at 800oC. Long-term redox testing over Ru impregnated LaFe0.375Mn0.625O3 indicated stable performance during the first 30 cycles following with a ~25% decrease in the activity during the last 70 cycles. Air treatment was effective to reactivate the redox catalyst. Detailed characterizations revealed the underlying mechanism for redox catalyst deactivation and reactivation. This study not only validated a DFT guided mixed oxide design strategy for CO2 utilization but also provides potentially effective approaches to enhance redox kinetics as well as long-term redox catalyst performance.