Harmonic analysis of symmetric random graphs
نویسندگان
چکیده
This note attempts to understand graph limits as defined by Lovasz and Szegedy (2006)} in terms of harmonic analysis on semigroups. is done representing probability distributions random exchangeable graphs mixtures characters the semigroup unlabeled with node-disjoint union, thereby providing an alternative derivation de Finetti's theorem for graphs.
منابع مشابه
Chromatic 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 کاملRandom approximation of a general symmetric equation
In this paper, we prove the Hyers-Ulam stability of the symmetric functionalequation $f(ph_1(x,y))=ph_2(f(x), f(y))$ in random normed spaces. As a consequence, weobtain some random stability results in the sense of Hyers-Ulam-Rassias.
متن کاملRandom Walks on Highly Symmetric Graphs
We consider uniform random walks on finite graphs with n nodes. When the hitting times are symmetric, the expected covering time is at least 89 log n O(n log log n) uniformly over all such graphs. We also obtain bounds for the covering times in terms of the eigenvalues of the transition matrix of the Markov chain. For distance-regular graphs, a general lower bound of ( n 1 ) l o g n is obtained...
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 کاملSymmetric Vertex Models on Planar Random Graphs
We discuss a 4-vertex model on an ensemble of 3-valent (Φ) planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The regular lattice equivalent of the model is the symmetric 8-vertex model on the honeycomb lattice, which can be mapped on to an Ising model in field, as was originally shown by Wu et.al. using generalised weak graph transformation technique...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kybernetika
سال: 2021
ISSN: ['1805-949X', '0023-5954']
DOI: https://doi.org/10.14736/kyb-2020-6-1081