Tetracyclic harmonic graphs
Tetrahedra on deformed spheres and integral group cohomology.
Tetravalent Arc-Transitive Graphs of Order 3p 2
Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p2 is given
Tetravalent half-arc-transitive graphs of order
We classify tetravalent -half-arc-transitive graphs of order , where and , are distinct odd primes. This result involves a subclass of tetravalent half-arc-transitive graphs of cube-free order.
Tetravalent non-normal Cayley graphs of order .
The 1 , 2 , 3-Conjecture And 1 , 2-Conjecture For Sparse Graphs
The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configurations cannot occur in minimal counterexamples to these conjectures. Discharging then confirms the conjectures...
The 11-element case of Frankl's conjecture.
The (16,6,2) designs.
The factor for multi-dimensional lattice paths with diagonal steps.
The 3-path-step operator on trees and unicyclic graphs
E. Prisner in his book Graph Dynamics defines the -path-step operator on the class of finite graphs. The -path-step operator (for a positive integer ) is the operator which to every finite graph assigns the graph which has the same vertex set as and in which two vertices are adjacent if and only if there exists a path of length in connecting them. In the paper the trees and the unicyclic graphs fixed in the operator are studied.
The 3-Rainbow Index of a Graph
Let G be a nontrivial connected graph with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ ℕ, where adjacent edges may be colored the same. A tree T in G is a rainbow tree if no two edges of T receive the same color. For a vertex subset S ⊆ V (G), a tree that connects S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such that there is a rainbow S-tree for each k-subset S of V (G) is called the k-rainbow index of G, denoted by rxk(G). In this paper,...
The isogonal sponges on the cubic lattice.
The 6 vertex model and Schubert polynomials.
The 99th Fibonacci identity.
The Abel-type polynomial identities.
The absence of efficient dual pairs of spanning trees in planar graphs.
The accessibility of finitely presented groups.
The Action of Nilpotent Groups on Infinite Graphs.
The active bijection between regions and simplices in supersolvable arrangements of hyperplanes.
The Acyclic Polynomial Of A Graph