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Abundance of information about the structure of a graph can be derived from the eigenvalues of its matrix representation. The eigenvalues are always connected to the characteristic polynomial of the matrix representation of a graph. In this paper, we discuss about the properties of adjacency matrix of the directed cyclic friendship graph, its cycle part is clockwise-oriented. By adding the values of the determinants of all directed cyclic induced subgraphs, the coefficients of the characteristic polynomial of the adjacency matrix of the directed cyclic friendship graph can be obtained. The real eigenvalues are obtained by factorization method, while the complex eigenvalues are obtained by root of complex number formula. [ABSTRACT FROM AUTHOR]

The aim of this study is to define a higher-order extension of the numbers arising from the finite sums containing higher powers of binomial coefficients. By using functional equations of the generating functions for these numbers, we derive some identities and relations between these numbers and λ-array polynomials. Finally, we give some remarks and observations on relations among the aforementioned numbers, λ-array polynomials and Eulerian type splines with their applications. [ABSTRACT FROM AUTHOR]

In this article, we use weighted sharing method to study the uniqueness results of differential polynomials containing L−function in the extended Selberg Class. [ABSTRACT FROM AUTHOR]

In the ring of quaternionic polynomials there is no easy solution to the problem of finding a suitable definition of multiplicity of a zero. In this paper we discuss different notions of multiple zeros available in the literature and add a computational point of view to this problem, by taking into account the behavior of the well known Newton's method in the presence of such roots. [ABSTRACT FROM AUTHOR]