Related papers: Higher-order Cheeger inequalities for graphons
To any graph we associate a sequence of integers called the gonality sequence of the graph, consisting of the minimum degrees of divisors of increasing rank on the graph. This is a tropical analogue of the gonality sequence of an algebraic…
We generalize the Cheeger inequality, a lower bound on the first nontrivial eigenvalue of a Laplacian, to the case of geometric sub-Laplacians on rank-varying Carnot-Carath\'eodory spaces and we describe a concrete method to lower bound the…
We investigate Cayley graphs of graph products by showing that graph products with vertex groups that have isomorphic Cayley graphs yield isomorphic Cayley graphs.
Guessing games for directed graphs were introduced by Riis for studying multiple unicast network coding problems. In a guessing game, the players toss generalised dice and can see some of the other outcomes depending on the structure of an…
In this paper we study spectra of Laplacians of infinite weighted graphs. Instead of the assumption of local finiteness we impose the condition of summability of the weight function. Such graphs correspond to reversible Markov chains with…
We derive Taylor's Formula for conformable fractional derivatives. This is then employed to extend some recent and classical integral inequalities to the conformable fractional calculus, including the inequalities of Steffensen, Chebychev,…
In this paper, we study the higher Steklov eigenvalues of graphs on surfaces. We obtain the upper bound of higher Steklov eigenvalues of a finite graph $G$ with boundary $B$ and genus $g$ by using metrical deformation via probability flows.…
An edge weighting problem of a graph G is an assignment of an integer weight to each edge e. Based on edge weighting problem, several types of vertex-coloring problems are put forward. A simple observation illuminates that edge weighting…
In this paper, we establish some new general Opial inequalities for Widder derivatives.
We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially…
We characterise gaps in the full homomorphism order of graphs.
We introduce the concept of pseudocover, which is a counterpart of cover, for symmetric graphs. The only known example of pseudocovers of symmetric graphs so far was given by Praeger, Zhou and the first-named author a decade ago, which…
The generalized conductance $\phi(G,H)$ between two graphs $G$ and $H$ on the same vertex set $V$ is defined as the ratio $$ \phi(G,H) = \min_{S\subseteq V} \frac{cap_G(S,\bar{S})}{ cap_H(S,\bar{S})}, $$ where $cap_G(S,\bar{S})$ is the…
In this article, we introduce a geometric and a spectral preorder relation on the class of weighted graphs with a magnetic potential. The first preorder is expressed through the existence of a graph homomorphism respecting the magnetic…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
The CD inequalities and CDE inequalities are useful in the estimate of curvature on graphs. This article is based on the ufinite graph with large girth, and finally concludes some curvature estimate in CD and CDE.
Given any two vertices u, v of a random geometric graph, denote by d_E(u,v) their Euclidean distance and by d_G(u,v) their graph distance. The problem of finding upper bounds on d_G(u,v) in terms of d_E(u,v) has received a lot of attention…
We improve upper bounds of F. R. K. Chung and of M. Lu, D. Wan, L.-P. Wang, X.-D. Zhang on the diameter of some Cayley graphs constructed from polynomials over finite fields.
Recent studies have highlighted significant fairness issues in Graph Transformer (GT) models, particularly against subgroups defined by sensitive features. Additionally, GTs are computationally intensive and memory-demanding, limiting their…
This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the…