Results 31 to 40 of about 101,413 (261)

ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS

Ural Mathematical Journal, 2023
Let \(\mathbb{C}^{m\times m}\) be the set of all \(m\times m\) matrices whose  entries are in \(\mathbb{C},\) the set of complex numbers. Then \(P(z):=\sum\limits_{j=0}^nA_jz^j,\) \(A_j\in \mathbb{C}^{m\times m},\) \(0\leq j\leq n\) is called a matrix ...
Zahid Bashir Monga, Wali Mohammad Shah
doaj   +1 more source

M-Polynomial of Product Graphs

CoRR
The 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, Mobeen Munir, Waqas Nazeer, Shazia Rafique, Shin Min Kang   +4 more
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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., Sitaramachandrarao, R.   +1 more
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M-polynomial Based Topological Analysis and Comparative Study of SiC3 Networks

Scientific Annals of Computer Science
Topological indices are numerical descriptors used in chemical graph theory to characterize the size, branching and connectivity of molecular structures.
Shibsankar Das, Shahzadi Nargis
doaj   +1 more source

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, Habib Mustafa, Zia Tariq Javeed, Naseem Asim, Hanif Anila, Ye Ansheng   +5 more
doaj   +1 more source

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, Nadeem Salamat, Riaz Hussain Khan, Ubaid ur Rehman Asghar, Md. Ashraful Alam, M. K. Pandit   +5 more
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Simple polynomial equations over (m x m)-matrices

Applied General Topology
Let 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 Dimensions
Topological 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, Aiman Ishtiaq, Misbah Rasheed   +2 more
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Neighborhood M-Polynomial of Crystallographic Structures

Biointerface Research in Applied Chemistry, 2020
The mathematical chemistry is wealthy, having tools such as polynomials and functions that can predict the properties of compounds. The M-polynomial is one of them which yields degree-based topological indices. In this work, we define the neighborhood M-polynomial to obtain neighborhood degree-based topological indices.
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