Harmonic Analysis on Metrized Graphs
نویسندگان
چکیده
This paper studies the Laplacian operator on a metrized graph, and its spectral theory.
منابع مشابه
The tau constant and the discrete Laplacian matrix of a metrized graph
Metrized graphs are finite graphs equipped with a distance function on their edges. For a metrized graph Γ, the tau constant τ(Γ) is an invariant which plays important roles in both harmonic analysis on metrized graphs and arithmetic of curves. T. Chinburg and R. Rumely [CR] introduced a canonical measure μcan of total mass 1 on a metrized graph Γ. The diagonal values of the Arakelov-Green’s fu...
متن کاملThe Tau Constant and the Edge Connectivity of a Metrized Graph
The tau constant is an important invariant of a metrized graph. It has connections to other graph invariants such as Kirchhoff index, and it has applications to arithmetic properties of algebraic curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We prove identities which we call “contraction”, “deletion”, and “contraction-deletion...
متن کاملThe Tau Constant of a Metrized Graph and its Behavior under Graph Operations
This paper concerns the tau constant, which is an important invariant of a metrized graph, and which has applications to arithmetic properties of curves. We give several formulas for the tau constant, and show how it changes under graph operations including deletion of an edge, contraction of an edge, and union of graphs along one or two points. We show how the tau constant changes when edges o...
متن کاملChromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs
In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...
متن کاملOn the harmonic index of bicyclic graphs
The harmonic index of a graph $G$, denoted by $H(G)$, is defined asthe sum of weights $2/[d(u)+d(v)]$ over all edges $uv$ of $G$, where$d(u)$ denotes the degree of a vertex $u$. Hu and Zhou [Y. Hu and X. Zhou, WSEAS Trans. Math. {bf 12} (2013) 716--726] proved that for any bicyclic graph $G$ of order $ngeq 4$, $H(G)le frac{n}{2}-frac{1}{15}$ and characterize all extremal bicyclic graphs.In this...
متن کامل