Related papers: Ramanujan Graphs
Throughout his entire mathematical life, Ramanujan loved to evaluate definite integrals. One can find them in his problems submitted to the \emph{Journal of the Indian Mathematical Society}, notebooks, Quarterly Reports to the University of…
Inspired by a very recent work of A. {\DH}uri\'c, S. Jev{\dj}eni\'c and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings, that includes all of the classical definitions already known in the literature. We…
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…
Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation,…
There has been a great deal of attention recently to graphs whose vertex set is a group, defined using the group structure. (The commuting graph, where two elements are joined if they commute, is the oldest and most famous example.) The…
In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several…
In this short note we use the umbral formalism to derive the Ramanujan Master Theorem and discuss its extension to more general cases.
This summarizes our latest understanding and results about the algorithms for enumerating Tanner Graphs that have a regular structure called Balanced Tanner Graphs. Enumeration algorithms for Balanced Tanner Graphs based upon Cyclic…
Knowledge Graphs are an emerging form of knowledge representation. While Google coined the term Knowledge Graph first and promoted it as a means to improve their search results, they are used in many applications today. In a knowledge…
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…
By defining grids as graphs, geometric graphs can be represented in a very concise way.
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
The presented work focuses on problems from determinant theory, set theory and topology. The term graph is the binding element that connects these problems. Graphs are distinguished by their geometrical simplicity, which helps in showing…
In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
The purpose of the present manuscript is to collect known results and present some new ones relating to nodal domains on graphs, with special emphasize on nodal counts. Several methods for counting nodal domains will be presented, and their…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
A conjecture regarding the structure of expander graphs is discussed.
In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…
In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs(digraphs). We obtain a new notion of the…