Results 41 to 50 of about 23,077,814 (292)
Note on the smallest root of the independence polynomial [PDF]
, 2013 One can define the independence polynomial of a graph G as follows. Let i(k)(G) denote the number of independent sets of size k of G, where i(0)(G) = 1. Then the independence polynomial of G is I(G,x) = Sigma(n)(k=0)(-1)(k)i(k)(G)x(k).
Csíkvári, Péter
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M-Polynomial of Product Graphs
CoRRThe M-polynomial provides a unifying framework for a wide class of degree-based topological indices. Despite its structural importance, general methods for computing the M-polynomial under graph constructions remain limited. In this paper, explicit formulas, and compact ones whenever possible, for the M-polynomial under different graph products whose ...
El-Mehdi Mehiri, Sandi Klavzar
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M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori [PDF]
Scientific Reports, 2017 AbstractV-Phenylenic nanotubes and nanotori are most comprehensively studied nanostructures due to widespread applications in the production of catalytic, gas-sensing and corrosion-resistant materials. Representing chemical compounds with M-polynomial is a recent idea and it produces nice formulas of degree-based topological indices which correlate ...
Young Chel Kwun +4 more
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A two-variable approach to solve the polynomial Lyapunov equation
, 2001 A two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is proposed. Lifting the problem from the one-variable to the two-variable context allows to use Faddeev-type recursions in order to solve the polynomial Lyapunov ...
Peeters, Ralf, Rapisarda, Paolo
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On the probability that the values of m polynomials have a given g.c.d.
Journal of Number Theory, 1987 Let \(m\geq 2\), \(h\geq 1\) be integers and \(f_ 1,...,f_ m\) be arbitrary polynomials with integer coefficients and of positive degree. The authors derive an asymptotic formula with an error term for \(M(x;f_ 1,...,f_ m;h),\) the number of m-tuples \(\) of positive integers such that \(g.c.d.(f_ 1(x_ 1),...,f_ m(x_ m))=h\) and each \(x_ i\leq x ...
Chidambaraswamy, J. +1 more
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M-polynomial Based Topological Analysis and Comparative Study of SiC3 Networks
Scientific Annals of Computer ScienceTopological indices are numerical descriptors used in chemical graph theory to characterize the size, branching and connectivity of molecular structures.
Shibsankar Das, Shahzadi Nargis
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Topological invariants for the line graphs of some classes of graphs
Open Chemistry, 2019 Graph theory plays important roles in the fields of electronic and electrical engineering. For example, it is critical in signal processing, networking, communication theory, and many other important topics.
Zhou Xiaoqing +5 more
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Computation of M-Polynomial and Topological Indices of Phenol Formaldehyde
Journal of Chemistry, 2022 Phenol formaldehyde (phenolic resin) has a wide range of moldings. However, it has immense consumption in manufacturing electrical equipment due to its insulating property. Phenolic resin retains properties at the freezing point, and also its age cannot be determined. Due to its insulator property, it has wide use in electrical equipment.
Muhammad Kamran +5 more
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Simple polynomial equations over (m x m)-matrices
Applied General TopologyLet m be any integer ≥ 3 . We consider the polynomial equation Xn+an-1·Xn-1+···+a1·X+a0·I=O, over (m x m)-matrices X with the real entries, where I is the identity matrix, O is the null matrix, ai ∈ ℝ for each i and n ≥ 1.
Vitalij Chatyrko, Alexandre Karassev
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Non-kekulean benzenoid hydrocarbon: physico-chemical properties for benzenoid hydrocarbon using topological indices and mpolynomial [PDF]
Computational Algorithms and Numerical DimensionsTopological indices are the numerical values that are connected to subatomic graphs in order to create the quantitative structure activity and structure attribute of a chemical compound and non-chemical graphs.
Anns Uzair +2 more
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