منابع مشابه
Counting Colorings of a Regular Graph
At most how many (proper) q-colorings does a regular graph admit? Galvin and Tetali conjectured that among all n-vertex, d-regular graphs with 2d|n, none admits more q-colorings than the disjoint union of n/2d copies of the complete bipartite graph Kd,d. In this note we give asymptotic evidence for this conjecture, showing that the number of proper q-colorings admitted by an n-vertex, d-regular...
متن کاملMaximizing H-Colorings of a Regular Graph
For graphs G and H, a homomorphism from G to H, or H-coloring of G, is an adjacency preserving map from the vertex set of G to the vertex set of H. Our concern in this paper is the maximum number of H-colorings admitted by an n-vertex, d-regular graph, for each H. Specifically, writing hom(G,H) for the number of H-colorings admitted by G, we conjecture that for any simple finite graph H (perhap...
متن کاملSymmetric Colorings Of Regular Polygons
It is calculated the number of symmetric r-colorings of vertices of a regular n-gon and the number of equivalence classes of symmetric r-colorings [1, 2]. A coloring is symmetric if it is invariant in respect to some mirror symmetry with an axis crossing center of polygon and one of its vertices. Colorings are equivalent if we can get one from another by rotating about the polygon center.
متن کاملIrregular colorings of regular graphs
An irregular coloring of a graph is a proper vertex coloring that distinguishes vertices in the graph either by their own colors or by the colors of their neighbors. In algebraic graph theory, graphs with a certain amount of symmetry can sometimes be specified in terms of a group and a smaller graph called a voltage graph. In [3], Radcliffe and Zhang found a bound for the irregular chromatic nu...
متن کاملCurvature from Graph Colorings
Given a finite simple graphG = (V,E) with chromatic number c and chromatic polynomial C(x). Every vertex graph coloring f of G defines an index if (x) satisfying the Poincaré-Hopf theorem [17] ∑ x if (x) = χ(G). As a variant to the index expectation result [19] we prove that E[if (x)] is equal to curvature K(x) satisfying Gauss-Bonnet ∑ xK(x) = χ(G) [16], where the expectation is the average ov...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2012
ISSN: 0364-9024
DOI: 10.1002/jgt.21658