Related papers: Roughness in Cayley Graphs
We introduce the notion of connection thickness of spheres in a Cayley graph, related to dead-ends and their retreat depth. It was well-known that connection thickness is bounded for finitely presented one-ended groups. We compute that for…
Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
We classify the planar cubic Cayley graphs of connectivity 2, providing an explicit presentation and embedding for each of them. Combined with [9] this yields a complete description of all planar cubic Cayley graphs.
Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case in which such graphs are Cayley graphs of Abelian groups. These groups can be constructed by…
This paper considers the edge-connectivity and restricted edge-connectivity of replacement product graphs, gives some bounds on edge-connectivity and restricted edge-connectivity of replacement product graphs and determines the exact values…
The theory of rough sets was firstly introduced by Pawlak (see \cite{p}). Many Mathematician has been studied the relations between rough sets and algebraic systems such as groups, rings and modules. In this paper we will introduce the…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…
Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article…
The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in…
Analysis of a network in terms of vulnerability is one of the most significant problems. Graph theory serves as a valuable tool for solving complex network problems, and there exist numerous graph-theoretic parameters to analyze the…
We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
We characterize the equivalence and the weak equivalence of Cayley graphs for a finite group $\C{A}$. Using these characterizations, we find enumeration formulae of the equivalence classes and weak equivalence classes of Cayley graphs. As…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…