Topological indices are the fixed numbers associated with the graphs. In recent years, mathematicians used indices to check the pharmacology characteristics and molecular behavior of medicines. In this article the first Zagreb connection number index is computed for the nanotubes VC5C7[ p, q] , HC5C7[ p,q] and Boron triangular Nanotubes. Also, the same index is computed for the Quadrilateral section $P_{m}^{n}$and $P_{m+\frac{1}{2}}^{n}$cuts from regular hexagonal lattices.

An outer-independent Italian dominating function (OIIDF) on a graph G with vertex set V (G) is defined as a function f : V (G) → {0, 1, 2}, such that every vertex v ∈ V (G) with f (v) = 0 has at least two neighbors assigned 1 under f or one neighbor w with f (w) = 2, and the set {u ∈ V | f (u) = 0} is independent. The weight of an OIIDF f is the value w(f) = u∈V (G) f (u). The minimum weight of an OIIDF on a graph G is called the outer-independent Italian domination number γ oiI (G) of G. In this paper, we initiate the study of the outer-independent Italian domination number and present the bounds on the outer-independent Italian domination number in terms of the order, diameter, and vertex cover number. In addition, we establish the lower and upper bounds on γ oiI (T) when T is a tree and characterize all extremal trees constructively. We also give the Nordhaus-Gaddum-type inequalities. INDEX TERMS Outer-independent Italian domination, Italian domination, trees.

In order to effectively extract features and improve classification accuracy for hyperspectral remote sensing images (HRSIs), the advantages of enhanced particle swarm optimization (PSO) algorithm, convolutional neural network (CNN), and extreme learning machine (ELM) are fully utilized to propose an innovative classification method of HRSIs (IPCEHRIC) in this paper. In the IPCEHRIC, an enhanced PSO algorithm (CWLPSO) is developed by improving learning factor and inertia weight to improve the global optimization performance, which is employed to optimize the parameters of the CNN in order to construct an optimized CNN model for effectively extracting the deep features of HRSIs. Then, a feature matrix is constructed and the ELM with strong generalization ability and fast learning ability is employed to realize the accurate classification of HRSIs. Pavia University data and actual HRSIs after Jiuzhaigou M7.0 earthquake are applied to test and prove the effectiveness of the IPCEHRIC. The experiment results show that the optimized CNN can effectively extract the deep features from HRSIs, and the IPCEHRIC can accurately classify the HRSIs after Jiuzhaigou M7.0 earthquake to obtain the villages, bareland, grassland, trees, water, and rocks. Therefore, the IPCEHRIC takes on stronger generalization, faster learning ability, and higher classification accuracy.

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