Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Linear Operators That Preserve the Genus of a Graph
View through CrossRef
A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k − 1 . A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k + 1 to graphs of genus k + 1 . We show that such linear operators are necessarily vertex permutations. Similar results with different restrictions on the genus k preserving operators give the same conclusion.
Title: Linear Operators That Preserve the Genus of a Graph
Description:
A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k − 1 .
A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph.
We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k + 1 to graphs of genus k + 1 .
We show that such linear operators are necessarily vertex permutations.
Similar results with different restrictions on the genus k preserving operators give the same conclusion.
Related Results
Graph convolutional neural networks for 3D data analysis
Graph convolutional neural networks for 3D data analysis
(English) Deep Learning allows the extraction of complex features directly from raw input data, eliminating the need for hand-crafted features from the classical Machine Learning p...
Bilangan Terhubung Titik Pelangi pada Graf Garis dan Graf Tengah dari Hasil Operasi Comb Graf Bintang C<sub>3</sub> dan Graf Bintang S<sub>n</sub>
Bilangan Terhubung Titik Pelangi pada Graf Garis dan Graf Tengah dari Hasil Operasi Comb Graf Bintang C<sub>3</sub> dan Graf Bintang S<sub>n</sub>
Penelitian ini bertujuan menentukan bilangan terhubung titik pelangi (rainbow vertex connection number) pada graf garis dan graf tengah yang diperoleh dari hasil operasi comb antar...
Bootstrapping a Biodiversity Knowledge Graph
Bootstrapping a Biodiversity Knowledge Graph
The "biodiversity knowledge graph" is a nice metaphor for connecting biodiversity data sources, but can we actually build it? Do we have sufficient linked data available? Given tha...
Abstract 902: Explainable AI: Graph machine learning for response prediction and biomarker discovery
Abstract 902: Explainable AI: Graph machine learning for response prediction and biomarker discovery
Abstract
Accurately predicting drug sensitivity and understanding what is driving it are major challenges in drug discovery. Graphs are a natural framework for captu...
Domination of Polynomial with Application
Domination of Polynomial with Application
In this paper, .We .initiate the study of domination. polynomial , consider G=(V,E) be a simple, finite, and directed graph without. isolated. vertex .We present a study of the Ira...
E-Cordial Labeling of Some Families of Graphs
E-Cordial Labeling of Some Families of Graphs
An E-cordial labeling σ: E →{0,1} induces σ∗: V →{0,1} on graph G=(V,E), where (σ(v)=(∑_(u∈V)▒〖σ(uv)〗) mod 2 is taken over all edges uv∈E, and the labelling satisfies the condition...
The quadrangle graph operator
The quadrangle graph operator
The cycle graph of a graph G is the graph [Formula: see text] whose vertices are the induced cycles of G and where two vertices are adjacent if and only if they are distinct induce...
A Scalable Data Structure for Efficient Graph Analytics and In-Place Mutations
A Scalable Data Structure for Efficient Graph Analytics and In-Place Mutations
The graph model enables a broad range of analysis, thus graph processing is an invaluable tool in data analytics. At the heart of every graph processing system lies a concurrent gr...