Related papers: Notes on $\omega$-graphs, reflexive $\omega$-graph…
We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.
In this paper, we introduce a method for finding all edge-transitive graphs of small order, using faithful representations of transitive permutation groups of small degree, and we explain how we used this method to find all edge-transitive…
We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent…
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…
Orthogonal Graph Representations are essential tools for testing existence of hidden variables in quantum theory. As required by the interpretation of Copenhaghe on the foundations of quantum mechanics, a physical observable is not…
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance…
We study topological properties of the graph topology.
Given a fixed integer $n$, we prove Ramsey-type theorems for the classes of all finite ordered $n$-colorable graphs, finite $n$-colorable graphs, finite ordered $n$-chromatic graphs, and finite $n$-chromatic graphs.
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
A consequence of Ore's classic theorem characterizing the maximal graphs with given order and diameter is a determination of the largest such graphs. We give a very short and simple proof of this smaller result, based on a well-known…
We construct explicit minimal models for the (hyper)operads governing modular, cyclic and ordinary operads, and wheeled properads, respectively. Algebras for these models are homotopy versions of the corresponding structures.
An embedding of a graph on an orientable surface is orientably-regular (or rotary, in an equivalent terminology) if the group of orientation-preserving automorphisms of the embedding is transitive (and hence regular) on incident vertex-edge…
We study invariants of virtual graphoids, which are virtual spatial graph diagrams with two distinguished degree-one vertices modulo graph Reidemeister moves applied away from the distinguished vertices. Generalizing previously known…
We classify the connected-homogeneous digraphs with more than one end. We further show that if their underlying undirected graph is not connected-homogeneous, they are highly-arc-transitive.
The interplay between groups and graphs have been the most famous and productive area of algebraic graph theory. In this paper, we introduce and study the graphs whose vertex set is group G such that two distinct vertices a and b having…
This paper investigates the new notion of $2$-word-$\pi$-repre\-sentable graphs: the nodes of the graph correspond to the letters of the two words and there exists an edge between two nodes if the projections of any two letters of both…
First, we give a functorial construction of a group associated to a symmetric operad. Applied to the endomorphism operad it gives the group of formal diffeomorphisms. Second, we associate a symmetric operad to any family of decorated graphs…
We establish several new $\Omega$-theorems for logarithmic derivatives of the Riemann zeta function and Dirichlet $L$-functions. In particular, this improves on earlier work of Landau (1911), Bohr-Landau (1913), and recent work of Lamzouri.
We study the inertia of distance matrices of weighted graphs. Our novel congruence-based proof of the inertia of weighted trees extends to a proof for the inertia of weighted unicyclic graphs whose cycle is a triangle. Partial results are…
In this largely expository paper, we will present a list of En -operads and give complete, and in some cases new, proofs of the equivalences between these operads.