During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predetermi...

In this paper, the Wiener Index ( ) ( ) { } ( ) ∑ ∈ = G V u v u v d G W , , and Hosoya polynomial ( ) ( ) { } ( ) ∑ ∈ = G V u v u v d x x G H , , , of a class of Jahangir graphs m J , 3 with exactly 1 3 + m vertices and m 4 edges are computed.

the invariant factors of its state-space matrix A + BF . This result can be seen as the solution of an inverse problem; that of finding a non-singular polynomial matrix with prescribed in‐ variant factors and left Wiener–Hopf factorization indices at infinity. To see this we recall that the invariant factors form a complete system of invariants for the finite equivalence of polynomial matrices ...

An efficient method for construction of J-unitary matrix polynomials is proposed, associated with companion functions the last row which a polynomial in 1/t. The relies on Wiener-Hopf factorization theory and stems from recently developed J-spectral algorithm certain Hermitian functions.

Let $G$ be a finite group. The intersection graph of is whose vertex set the all proper non-trivial subgroups and two distinct vertices $H$ $K$ are adjacent if only $H\cap K \neq \{e\}$, where $e$ identity group $G$. In this paper, we investigate some properties exploring topological indices such as Wiener, Hyper-Wiener, first second Zagreb, Schultz, Gutman eccentric connectivity $D_{2n}$ for $...

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. We apply our criterion to problems in Fourier analysis on projective/in...

Stability and performance of a system can be inferred from the evolution of statistical characteristic (i.e. mean, variance...) of system states. The polynomial chaos of Wiener provides a computationally effective framework for uncertainty quantification of stochastic dynamics in terms of statistical characteristic. In this work, polynomial chaos is used for uncertainty quantification of fracti...

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. We apply our criterion to problems in Fourier analysis on projective/in...