Categorical constructions in graph theory.
Categorification of Hopf algebras of rooted trees
We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec ℕ) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to ℤ and collapsing H 0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring...
Caterpillars
Cayley color graphs of inverse semigroups and groupoids
The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.
Cayley graphs on the symmetric group generated by initial reversals have unit spectral gap.
Centers and centroids of unicyclic graphs
Centers in iterated line graphs.
Centers in line graphs
Centers of directed cacti
Centers of n-fold tensor products of graphs
Formulas for vertex eccentricity and radius for the n-fold tensor product of n arbitrary simple graphs are derived. The center of G is characterized as the union of n+1 vertex sets of form V₁×V₂×...×Vₙ, with .
Centralité et compacité d'un graphe
Un grand nombre de situations de psychologie sociale peuvent être interprétées en termes de graphe, notamment celles qui traitent des phénomènes de relation et de communication. Les travaux de A. Bavelas et H. Leavitt ont révélé l'influence des différents types de réseaux sur le comportement des groupes ; ils ont mis en pleine lumière l'intérêt de la notion de centralité. Les recherches de C. Flament ont enrichi et fortement nuancé ces résultats en faisant apparaître le poids de la nature de la...
Centrally-symmetric tight surfaces and graph embeddings.
Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes
The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.
Certain cubic multigraphs and their upper embeddability
Certain new M-matrices and their properties with applications
The Mₙ-matrix was defined by Mohan [21] who has shown a method of constructing (1,-1)-matrices and studied some of their properties. The (1,-1)-matrices were constructed and studied by Cohn [6], Ehrlich [9], Ehrlich and Zeller [10], and Wang [34]. But in this paper, while giving some resemblances of this matrix with a Hadamard matrix, and by naming it as an M-matrix, we show how to construct partially balanced incomplete block designs and some regular graphs by it. Two types of these M-matrices...
Certificates of factorisation for a class of triangle-free graphs.
Certificates of factorisation for chromatic polynomials.
Chaines maximales de préordres.
Chains, subwords, and fillings: strong equivalence of three definitions of the Bruhat order.
Changing of the domination number of a graph: edge multisubdivision and edge removal