Bimetallic clusters have aroused increased attention because of the ability to tune their own properties by changing size, shape, and doping. in present work, a structural search of the global minimum for divalent bimetal Be 2 Mg n (n = 1-20) clusters are performed by utilizing CALYPSO structural searching method with subsequent Dft optimization. We investigate the evolution of geometries, electronic properties, and nature of bonding from small to medium-sized clusters. it is found that the structural transition from hollow 3D structures to filled cage-like frameworks emerges at n = 10 for Be 2 Mg n clusters, which is obviously earlier than that of Mg n clusters. the Be atoms prefer the surface sites in small cluster size, then one Be atom tend to embed itself inside the magnesium motif. At the number of Mg larger than eighteen, two Be atoms have been completely encapsulated by caged magnesium frameworks. in all Be 2 Mg n clusters, the partial charge transfer from Mg to Be takes place. An increase in the occupations of the Be-2p and Mg-3p orbitals reveals the increasing metallic behavior of Be 2 Mg n clusters. the analysis of stability shows that the cluster stability can be enhanced by Be atoms doping and the Be 2 Mg 8 cluster possesses robust stability across the cluster size range of n = 1-20. There is s-p hybridization between the Be and Mg atoms leading to stronger Be-Mg bonds in Be 2 Mg 8 cluster. this finding is supported by the multi-center bonds and Mayer bond order analysis.
Scientific RepoRtS |(2020) 10:6052 | https://doi.
Let G be a connected graph and d(µ, ω) be the distance between any two vertices of G. The diameter of G is denoted by diam(G) and is equal to max{d(µ, ω); µ, ω ∈ G}. The radio labeling (RL) for the graph G is an injective function : V (G) → N ∪ {0} such that for any pair of vertices µ andThe span of radio labeling is the largest number in (V ). The radio number of G, denoted by rn(G) is the minimum span over all radio labeling of G. In this paper, we determine radio number for the generalized Petersen graphs, P(n, 2), n = 4k +2. Further the lower bound of radio number for P(n, 2) when n = 4k is determined.INDEX TERMS Diameter, radio number, generalized Petersen graph.
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