We apply Alexandrov geometry methods to study geometric analysis aspects of infinite
semiplanar graphs with nonnegative combinatorial curvature. We obtain the metric …

Structural topology constraints in topology optimization are an important research topic. The
structural topology is characterized by the topological invariance of the number of holes. The …

We introduce a curvature function for planar graphs to study the connection between the
curvature and the geometric and spectral properties of the graph. We show that non-positive …

We study the p-independence of spectra of Laplace operators on graphs arising from
regular Dirichlet forms on discrete spaces. Here, a sufficient criterion is given solely by a …

The connective constant μ (G) of a graph G is the exponential growth rate of the number of
self-avoiding walks starting at a given vertex. We investigate the validity of the inequality μ≥ …

Let $ M $ be a connected $ d $-manifold without boundary obtained from a (possibly infinite)
collection $\mathcal P $ of polytopes of ${\mathbb R}^ d $ by identifying them along …

Let G be an infinite graph embedded in a surface such that each open face of the
embedding is homeomorphic to an open disk and is bounded by finite number of edges. For …

For a connected simple graph embedded into a 2-sphere, we show that the number of
vertices of the graph is less than or equal to 380 if the degree of each vertex is at least three …

arXiv:1608.07000v1 [math.CO] 25 Aug 2016 Page 1 GRAPHS WITH LARGE GIRTH AND
NONNEGATIVE CURVATURE DIMENSION CONDITION BOBO HUA AND YONG LIN Abstract …

In this paper, we prove that any simple $\{C_3, C_5\} $-free non-empty connected graph $ G
$ with LLY curvature bounded below by $\kappa> 0$ has the order at most $2^{\frac …