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The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. Th...

In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number Fn+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pe...

In this paper, by using identities related to the tessarines, Fibonacci numbers and Lucas we define tessarines tessarines. We obtain Binet formulae, D’ocagnes identity Cassini for these also give of negatessarines new vector which are called tessarine vector.

We study the extended Frobenius problem for sequences of form $\{f_a+f_n\}_{n\in\mathbb{N}}$, where $\{f_n\}_{n\in\mathbb{N}}$ is Fibonacci sequence and $f_a$ a number. As consequence, we show that family numerical semigroups associated to these satisfies Wilf's conjecture.

The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees with n edges and Fibonacci number > 2n−1 + 5 have diameter ≤ 4 and determine the order of these trees with respect to their Fibonacci numbers. Furthermore, it is shown that the average Fibonacci number of a star-like ...

A subset S of vertices in a graph G is said to be an independent set of G if each edge in the graph has at most one endpoint in S and a set W ( V is said to be a resolving set of G, if the vertices in G have distinct representations with respect to W. A resolving set W is said to be an independent resolving set, or an ir-set, if it is both resolving and independent. The minimum cardinality of W...

A subset S of vertices in a graph G is said to be an independent set of G if each edge in the graph has at most one endpoint in S and a set W ( V is said to be a resolving set of G, if the vertices in G have distinct representations with respect to W. A resolving set W is said to be an independent resolving set, or an ir-set, if it is both resolving and independent. The minimum cardinality of W...