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Residual Closeness of Graphs with Given Parameters
Robustness of the network topology is a key aspect in the design of computer networks. Residual closeness is a new graph-theoretic concept defined as...
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Ricci-flat Graphs with Girth Four
Lin-Lu-Yau introduced a notion of Ricci curvature for graphs and obtained a complete classification for all Ricci-flat graphs with girth at least...
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Quantitative Russo–Seymour–Welsh for Random Walk on Random Graphs and Decorrelation of Uniform Spanning Trees
We prove a quantitative Russo–Seymour–Welsh (RSW)-type result for random walks on two natural examples of random planar graphs: the supercritical...
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\(\alpha _i\) -Metric Graphs: Radius, Diameter and all Eccentricities
We extend known results on chordal graphs and distance-hereditary graphs to much larger graph classes by using only a common metric property of these...
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Geoffrey Exoo and Dan Ismailescu, or 2 Men for 2 Forbidden Distances
We have a team of a Geombinatorics Editor Geoffrey Exoo and Dan Ismailescu. You may recall Chap. 16 of...
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Overview of the Topical Collection: Harmonic Analysis on Combinatorial Graphs
This topical collection “Harmonic Analysis on Combinatorial Graphs” contains 20 papers devoted to a very broad range of themes written by pure and...
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Spotted disk and sphere graphs. II
The disk graph of a handlebody H of genus g ≥ 2 with m ≥ 0 marked points on the boundary is the graph whose vertices are isotopy classes of disks...
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Assignment of orthologous genes in unbalanced genomes using cycle packing of adjacency graphs
The adjacency graph is a structure used to model genomes in several rearrangement distance problems. In particular, most studies use properties of a...
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Green functions and smooth distances
In the present paper, we show that for an optimal class of elliptic operators with non-smooth coefficients on a 1-sided Chord-Arc domain, the...
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Distance signless Laplacian spectral radius for the existence of path-factors in graphs
Let G be a connected graph of order n , where n is a positive integer. A spanning subgraph F of G is called a path-factor if every component of F is a...
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The Explorer–Director Game on Graphs
The Explorer-Director game , first introduced by Nedev and Muthukrishnan, can be described as a game where two players—Explorer and Director—determine...
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High-girth near-Ramanujan graphs with localized eigenvectors
We show that for every prime d and α ∈ (0, 1/6), there is an infinite sequence of ( d + 1)-regular graphs G = ( V, E ) with high girth Ω(α log d (∣ V ∣),...
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Maximum weight disjoint paths in outerplanar graphs via single-tree cut approximators
Since 1997 there has been a steady stream of advances for the maximum disjoint paths problem. Achieving tractable results has usually required...
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Spectra of Variants of Distance Matrices of Graphs and Digraphs: A Survey
Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive...
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Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules
In this paper, we establish explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In...
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The Oriented Diameter of Graphs with Given Connected Domination Number and Distance Domination Number
Let G be a bridgeless graph. An orientation of G is a digraph obtained from G by assigning a direction to each edge. The oriented diameter of G is...
