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Two-geodesic-transitive Graphs and Vertex-transitive Diameter Two Hexavalent Graphs
In this paper, we first investigate the family of vertex-transitive diameter 2 hexavalent graphs and particularly completely determine such graphs...
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Cubic Vertex-Transitive Graphs Admitting Automorphisms of Large Order
A connected graph of order n admitting a semiregular automorphism of order n / k is called a k -multicirculant. Highly symmetric multicirculants of...
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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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Vertex-transitive Diameter Two Graphs
We investigate the family of vertex-transitive graphs with diameter 2. Let Γ be such a graph. Suppose that its automorphism group is transitive on...
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Nowhere-zero 3-flows in nilpotently vertex-transitive graphs
We prove that every regular graph of valency at least four whose automorphism group contains a nilpotent subgroup acting transitively on the vertex...
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Presentations for vertex-transitive graphs
We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than...
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On the Number of Fixed Points of Automorphisms of Vertex-Transitive Graphs
The main result of this paper is that, if Γ is a finite connected 4-valent vertex- and edge-transitive graph, then either Γ is part of a...
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Resolving The Hamiltonian Problem for Vertex-Transitive Graphs of Order a Product of Two Primes
A step forward is made in a long standing Lovász problem regarding existence of Hamilton paths in vertex-transitive graphs. It is shown that a...
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A Finitary Structure Theorem for Vertex-Transitive Graphs of Polynomial Growth
We prove a quantitative, finitary version of Trofimov’s result that a connected, locally finite vertex-transitive graph Γ of polynomial growth admits...
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A Graph with a Locally Projective Vertex-Transitive Group of Automorphisms Aut(\(Fi_{22}\)) Which Has a Nontrivial Stabilizer of a Ball of Radius \(2\)
Earlier, to confirm that one of the possibilities for the structure of vertex stabilizers of graphs with projective suborbits is realizable, we...
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The Simultaneous Fractional Dimension of Graph Families
For a connected graph G with vertex set V , let R G { x, y } = { z ∈ V : d G ( x, z ) ≠ d G ( y, z )} for any distinct x, y ∈ V , where d G ( u, w ) denotes the length...
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On Tetravalent Vertex-Transitive Bi-Circulants
A graph Γ is called a bi-circulant if it admits a cyclic group as a group of automorphisms acting semiregularly on the vertices of Γ with two orbits....
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Exploring the SDE index: a novel approach using eccentricity in graph analysis
In this article, we present an enhanced version of the symmetric division deg index ( sdd -index) known as symmetric division eccentric index or SDE ...
