Related papers: Fibonacci Graphs and their Expressions
The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a Fibonacci graph which gives a generic example of non-series-parallel graphs. Our intention in this paper is to simplify the…
The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a full square rhomboid that is an example of non-series-parallel graphs. Our intention is to simplify the expressions of full square…
The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a square rhomboid that is an example of non-series-parallel graphs. Our intention is to simplify the expressions of square rhomboids…
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many…
In this paper we study some properties of Fibonacci-sum set-graphs. The aforesaid graphs are an extension of the notion of Fibonacci-sum graphs to the notion of set-graphs. The colouring of Fibonacci-sum graphs is also discussed. A number…
The optimal calculation order of a computational graph can be represented by a set of algebraic expressions. Computational graph and algebraic expression both have close relations and significant differences, this paper looks into these…
The $d$-Fibonacci digraphs $F(d,k)$, introduced here, have the number of vertices following generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their…
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…
A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…
We provide a new perspective on the divisor theory of graphs, using additive combinatorics. As a test case for this perspective, we compute the gonality of certain families of outerplanar graphs, specifically the strip graphs. The Jacobians…
Among the classical models for interconnection networks are hypercubes and Fibonacci cubes. Fibonacci cubes are induced subgraphs of hypercubes obtained by restricting the vertex set to those binary strings which do not contain consecutive…
In this paper, we define the bi-periodic Fibonacci matrix sequence that represent bi-periodic Fibonacci numbers. Then, we investigate generating function, Binet formula and summations of bi-periodic Fibonacci matrix sequence. After that, we…
Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we investigate relationships between one type of graph and well-known Fibonacci sequence. In this content, we…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
The Fibonacci dimension fdim(G) of a graph G is introduced as the smallest integer f such that G admits an isometric embedding into Gamma_f, the f-dimensional Fibonacci cube. We give bounds on the Fibonacci dimension of a graph in terms of…
Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their endpoints in a network-like fashion. Here we propose an…
One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer…
Threshold graphs are a prevalent and widely studied class of simple graphs. They have several equivalent definitions which makes them a go-to class for finding examples and counter examples when testing and learning. This versatility has…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…