Related papers: Some Euler-type formulas for planar graphs
Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.
Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…
We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…
Besides the need for a better understanding of networks, there is a need for prescriptive models and tools to specify requirements concerning networks and their associated graph representations. We propose class-based graphs as a means to…
In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between…
Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
We examine connections between the gonality, treewidth, and orientable genus of a graph. Especially, we find that hyperelliptic graphs in the sense of Baker and Norine are planar. We give a notion of a bielliptic graph and show that each of…
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…
In this paper, we construct the "2221" subfactor planar algebra by finding it as a subalgebra of the graph planar algebra of its principal graph. In particular, we give a presentation of the "2221" subfactor planar algebra consisting of…
We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at…
We give a formula for computing the characteristic polynomial for certain hyperplane arrangements in terms of the number of bipartite graphs of given rank and cardinality.
This paper describes a new approach to the problem of generating the class of all geodetic graphs homeomorphic to a given geodetic one. An algorithmic procedure is elaborated to carry out a systematic finding of such a class of graphs. As a…
Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.
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…
This extended abstract introduces a class of graph learning applicable to cases where the underlying graph has polytopic uncertainty, i.e., the graph is not exactly known, but its parameters or properties vary within a known range. By…
We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie…
A few properties of unitary Cayley graphs are explored using their eigenvalues. It is shown that the adjacency algebra of a unitary Cayley graph is a coherent algebra. Finally, a class of unitary Cayley graphs that are distance regular are…
For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…
In this work we develop a theory of hierarchical clustering for graphs. Our modeling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons…