This new topological invariant is applied in the areas of chemical graph theory. In this paper we have obtained Sombor index m−shadow graphs path Dm(Pn), cycle Dm(Cn), ladder Dm(Ln) and tadpole Dm(Tn,p). We also concluded that, m-shadow any regular or finite connected G SO(G)m3

We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized star product approach. We give several examples and show how they generalize some of the scattering matrices computed in the mathematical or condensed matter ...

We study a class of Labelled Oriented Graph (LOG) group where the underlying graph is a tadpole graph. We show that such a group is the natural HNN extension of a cyclically presented group and investigate the relationship between the LOG group and the cyclically presented group. We relate the second homotopy groups of their presentations and show that hyperbolicity of the cyclically presented ...

The hitting time, huv , of a random walk on a finite graph G, is the expected time for the walk to reach vertex v given that it started at vertex u. We present two methods of calculating the hitting time between vertices of finite graphs, along with applications to specific classes of graphs, including grids, trees, and the ’tadpole’ graphs. keywords: random walks, hitting time

A major application of the mathematical concept graph in quantum mechanics is to model networks electrical wires or electromagnetic wave-guides. In this paper, we address dynamics a particle trapped on such network presence an external field. We study controllability motion when intensity field changes over time and plays role control. From point view, modeled by so-called bilinear Schrödinger ...

A parallel variant of breadth-rst search for distributed computing is presented. The variant allows exhaustive enumeration of elements of a search space (implicitly deened graph) in which the representation of all graph nodes would otherwise require more than the total available memory. This algorithm requires the use of a tadpole data structure to partition the search space into connected subg...

Predation and competition can induce important density- and trait-mediated effects on species, with implications for community stability. However, interactions of these factors with parasitism remain understudied. Here we investigate interactions among competition, predation and parasitism by crossing tadpole density (Bufo americanus), presence of a caged predator (Notophthalmus viridescens), a...

If G is a connected graph with vertex set V , then the eccentric connectivity index of G, ξ(G) is defined as ∑ deg(v).ec(v) where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. The Wiener index W (G) = 1 2 [ ∑ d(u, v)], the hyper-Wiener index WW (G) = 1 2 [ ∑ d(u, v) + ∑ d(u, v)] and the reverseWiener index ∧(G) = n(n−1)D 2 −W (G), where d(u, v) is the distance of two vertice...