Open AccessThe surjectivity of the combinatorial Laplacian on infinite graphs
Author(s) -
Tullio CeccheriniSilberstein,
Michel Coornaert,
Józef Dodziuk
Publication year - 2012
Publication title -
l’enseignement mathématique
Language(s) - English
Resource type - Journals
eISSN - 2309-4672
pISSN - 0013-8584
DOI - 10.4171/lem/58-1-5
Subject(s) - surjective function , mathematics , combinatorics , vertex (graph theory) , graph , laplace operator , laplacian matrix , discrete mathematics , mathematical analysis
Given a connected locally finite simplicial graph $ G$ with vertex set $V$, the combinatorial Laplacian $\Delta_G \colon \R^V \to \R^V$ is defined on the space of all real-valued functions on $V$. We prove that $\Delta_G$ is surjective if $G$ is infinite.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom