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This talk will introduce some topics related to the study of nonlinear Schr?dinger equation on metric graphs, and then show the existence result of concentrated solutions to NLS equations on compact g...
Turán-type problem may be one of central problems in extremal graph theory. Particularly, the Turán number of a cycle attracts much attention. In this talk, we introduce a terminology, that is, theta ...
Cayley graphs form an important class of vertex-transitive graphs, which have been the object of study for many decades. These graphs admit a group of automorphisms that acts regularly (sharply-transi...
Nowadays "colored notions of connectivity in graphs" becomes a new and active subject in graph theory. Starting from rainbow connection, monochromatic connection and proper connection appeared later. ...
Curvature is a notion originally developed in differential and Riemannian geometry. It was then discovered that curvature inequalities in Riemannian manifolds are equivalent to other geometric propert...
Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Mar...
The orientation preserving topological symmetry group of a graph embedded in the 3-sphere is the subgroup of the automorphism group of the graph consisting of those automorphisms which can be induc...
We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group An which is not the topological symmetry group of any graph embedded in the manifold. ...
We present an adaptive finite element method (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C 1 graphs Γ in R d (d ≥ 2). We first derive residual-type a posteri...
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
Given a sequence {αn} in (0, 1) converging to a rational, we examine the model theoretic properties of structures obtained as limits of ShelahSpencer graphs G(m, m−αn ). We show that in most c...
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G* such that T and T* do not intersect. We show that it is not always possible to find T in ...
We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SLn(Z/kZ) with respect to a standard two-element generating set, is at most a constant times n2 ln k. This answers a ques...
We give a non-deterministic algorithm that expresses elements of SLN(Z), for N>2, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We sh...
We pose some graph theoretic conjectures about duality and the diameter of maximal trees in planar graphs, and we describe innovations in the following two topics in Geometric Group Theory, where the ...

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