On the k-Mersenne–Lucas numbers

The minus k-domination numbers in graphs

For any integer  ‎, ‎a minus  k-dominating function is a‎function  f‎ : ‎V (G)  {-1,0‎, ‎1} satisfying w) for every  vertex v, ‎where N(v) ={u V(G) | uv  E(G)}  and N[v] =N(v)cup {v}. ‎The minimum of ‎the values of  v)‎, ‎taken over all minus‎k-dominating functions f,‎ is called the minus k-domination‎number and is denoted by $gamma_k^-(G)$ ‎. ‎In this paper‎, ‎we ‎introduce the study of minu...

On the k-Lucas Numbers

From a special sequence of squares of k-Fibonacci numbers, the kLucas sequences are obtained in a natural form. Then, we will study the properties of the k-Lucas numbers and will prove these properties will be related with the k-Fibonaci numbers. In this paper we examine some of the interesting properties of the k-Lucas numbers themselves as well as looking at its close relationship with the k-...

On k-planar crossing numbers

The k-planar crossing number of a graph is the minimum number of crossings of its edges over all possible drawings of the graph in k planes. We propose algorithms and methods for k-planar drawings of general graphs together with lower bound techniques. We give exact results for the k-planar crossing number ofK2k+1,q , for k 2.We prove tight bounds for complete graphs.We also study the rectiline...

On the Properties of k-Fibonacci Numbers

On the complex k-Fibonacci numbers

Abstract: We first study the relationship between the k-Fibonacci numbers and the elements of a subset of Q. Later, and since generally studies that are made on the Fibonacci sequences consider that these numbers are integers, in this article, we study the possibility that the index of the k-Fibonacci number is fractional; concretely, 2n+1 2 . In this way, the k-Fibonacci numbers that we obtain...