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On Directed and Undirected Diameters of Vertex-Transitive Graphs
A directed diameter of a directed graph is the maximum possible distance between a pair of vertices, where paths must respect edge orientations,...
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Identifiability of local and global features of phylogenetic networks from average distances
Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The...
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Vector-relation configurations and plabic graphs
We study a simple geometric model for local transformations of bipartite graphs. The state consists of a choice of a vector at each white vertex made...
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Signed Zero-Divisor Graphs Over Commutative Rings
In this paper, we define signed zero-divisor graphs over commutative rings and investigate the interplay between the algebraic properties of the...
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In The Beginning: Roots of Domination in Graphs
While domination in graphs was first formally defined by Berge in 1958, the roots of domination can be traced back to defense strategies used by the...
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The Cheeger cut and Cheeger problem in metric graphs
For discrete weighted graphs there is sufficient literature about the Cheeger cut and the Cheeger problem, but for metric graphs there are few...
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Wiener index of generalized odd complete graphs
The Wiener index W ( G ) of a graph G is the sum of distances between all pairs of vertices of a connected graph. Motivated by the definition of an odd...
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Order Distances and Split Systems
Given a pairwise distance
D on the elements in a finite setX , the order distance Δ(D) onX is defined by first associating a total preorder ≼ x onX ...