Topology of Cell-Aggregated Planar Graphs
نویسندگان
چکیده
We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k = 3 per node. The emergent graph structures are controlled by two parameters—chemical potential of the cell aggregation and the width of the cell size distribution. We compute several statistical properties of these graphs—fractal dimension of the perimeter, distribution of shortest paths between pairs of nodes and topological betweenness of nodes and links. We show how these topological properties depend on the control parameters of the aggregation process and discuss their relevance for the conduction of current in self-assembled nanopatterns.
منابع مشابه
$n$-Array Jacobson graphs
We generalize the notion of Jacobson graphs into $n$-array columns called $n$-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an $n$-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.
متن کاملAn Alexandroff topology on graphs
Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...
متن کاملOn the M-polynomial of planar chemical graphs
Let $G$ be a graph and let $m_{i,j}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The $M$-polynomial of $G$ is $M(G;x,y) = sum_{ile j} m_{i,j}(G)x^iy^j$. With $M(G;x,y)$ in hands, numerous degree-based topological indices of $G$ can be routinely computed. In this note a formula for the $M$-polynomial of planar (chemical) graphs which have only vertices...
متن کاملPlanar Graphs as L-intersection or L-contact graphs
The x-intersection graphs are the graphs that have a representation as intersection graphs of axis parallel x shapes in the plane. A subfamily of these graphs are {x, |,−}-contact graphs which are the contact graphs of axis parallel x, |, and − shapes in the plane. We prove here two results that were conjectured by Chaplick and Ueckerdt in 2013. We show that planar graphs are x-intersection gra...
متن کاملALTERNATING KNOTS, PLANAR GRAPHS AND q-SERIES
Recent advances in Quantum Topology assign q-series to knots in at least three different ways. The q-series are given by generalized Nahm sums (i.e., special qhypergeometric sums) and have unknown modular and asymptotic properties. We give an efficient method to compute those q-series that come from planar graphs (i.e., reduced Tait graphs of alternating links) and compute several terms of thos...
متن کامل