The energy of a simple connected graph G is equal to the sum of the absolute value of eigenvalues of the graph G where the eigenvalue of a graph G is the eigenvalue of its adjacency matrix AG. Ultimately, scores of various graph energies have been originated. It has been shown in this paper that the different graph energies of the regular splitting graph S′G is a multiple of corresponding energy of a given graph G.

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In this paper, we investigate the system undergoes flip and Neimark Sacker bifurcation in the interior of R 2 + by using the center manifold theorem and bifurcation theory. The dynamics of this discrete time predator-pre model is investigated in the closed first quadrant of R 2 +. INDEX TERMS Flip and Neimark sacker bifurcation, time predator-pre model, manifold.

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.

In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for  γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivided hexagonal network, subdivided backbone DNA network, and subdivided honeycomb network. The discussion on the aforementioned networks will give us very remarkable results by using the aforementioned topological indices.