Related papers: Higher diameters of Cayley digraphs
A kei on $[n]$ can be thought of as a set of maps $(f_x)_{x \in [n]}$, where each $f_x$ is an involution on $[n]$ such that $(x)f_x = x$ for all $x$ and $f_{(x)f_y} = f_yf_xf_y$ for all $x$ and $y$. We can think of kei as loopless,…
In this paper,we construct some directed strongly regular Cayley graphs on dihedral groups,these generalizes some earlier constructions.We also characterize some certain directed strongly regular Cayley graphs on dihedral groups…
Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.
Radial Moore graphs and digraphs are extremal graphs related to the Moore ones where the distance-preserving spanning tree is preserved for some vertices. This leads to classify them according to their proximity to being a Moore graph or…
In this contribution we present a construction of large networks of diameter two and of order $\frac{1}{2}d^2$ for every degree $d\geq 8$, based on Cayley graphs with surprisingly simple underlying groups. For several small degrees we…
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.
We study topological properties of the graph topology.
We classify the distance-regular Cayley graphs with least eigenvalue $-2$ and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain…
In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent)…
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
In this paper we give graphs with the largest known order for a given degree $\Delta$ and diameter $D$. The graphs are constructed from Moore bipartite graphs by replacement of some vertices by adequate structures. The paper also contains…
Researchers in the past have studied eigenvalues of Cayley digraphs or graphs. We are interested in characterizing Cayley digraphs on a finite Abelian group G whose eigenvalues are algebraic integers in a given number field K. And we…
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
In this paper, we define irregular bipolar fuzzy graphs and its various classifications. Size of regular bipolar fuzzy graphs is derived. The relation between highly and neighbourly irregular bipolar fuzzy graphs are established. Some basic…
In this paper we will give the calculus, the criterion, and the existence of the arithmetic Galois covers of higher relative dimensions.
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
We define and study graphs associated to hexagon decompositions of surfaces by curves and arcs. One of the variants is shown to be quasi-isometric to the pants graph, whereas the other variant is quasi-isometric to (a Cayley graph of) the…
This manuscript introduces Diophantine labeling, a new way of labeling of the vertices for finite simple undirected graphs with some divisibility condition on the edges. Maximal graphs admitting Diophantine labeling are investigated and…
We obtain sharp upper and lower bounds for the diameter of Ricci-flat Kahler metrics on polarized Calabi-Yau degeneration families, as conjectured by Kontsevich-Soibelman.
We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have concentrated mainly on the diameter 2 case.…