The One-Path Laplacian Operator on Locally Infinite Graph
Abstract
In this article, we extend the one-path Laplacian operator to consider infinite graphs that are connected and locally finite. In particular, we focus our attention on the some of the main properties of this operator, such as the essentially self-adjointness and the boundedness. We first proved analytically that this operator is symmetric and non-negative, which necessarily means that it is essentially self-adjoint. Then, we proved analytically that the one-path Laplacian operator is bounded.