A binary modified de Bruijn sequence is an infinite and periodic derived by removing a zero from the longest run of zeros in sequence. The minimal polynomial its unique least-degree characteristic polynomial. Leveraging recent characterization, we devise novel general approach to determine We translate characterization into problem identifying Hamiltonian cycle specially constructed graph. grap...

The Wiener matrix and the hyper-Wiener number of a tree (acyclic structure), higher Wiener numbers of a tree that can be represented by a Wiener number sequence W, W,W.... whereW = W is the Wiener index, and R W k K    ,.... 2 , 1 is the hyper-Wiener number. The concepts of the Wiener vector and hyper-Wiener vector of a graph are introduced for the molecular graph of bi-phenylene. Moreover, ...

Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

Fibonacci polynomial sequence is an extension of sequence. Here we define a generalizing the integer which enumerates number subsets set [n] including no two consecutive even integers. The associated with polynomials. Some basic properties are obtained.