Enumeration of graphs maximal with respect to connectivity
Enumeration of Hamiltonian circuits in rectangular grids.
Enumeration of hamiltonian paths in Caley diagrams.
Enumeration of perfect matchings of a type of quadratic lattice on the torus.
Enumeration of tilings of diamonds and hexagons with defects.
Enumeration of unigraphical partitions.
Enumeration problems of trees. (Abzählprobleme bei Bäumen.)
Enumeration under group action
Enumerative formulae for unrooted planar maps: a pattern.
Enumerative problems inspired by Mayer's theory of cluster integrals.
Equations relating factors in decompositions into factors of some family of plane triangulations, and applications (with an appendix by Andrzej Schinzel)
Let be the family of all 2-connected plane triangulations with vertices of degree three or six. Grünbaum and Motzkin proved (in dual terms) that every graph P ∈ has a decomposition into factors P₀, P₁, P₂ (indexed by elements of the cyclic group Q = 0,1,2) such that every factor consists of two induced paths of the same length M(q), and K(q) - 1 induced cycles of the same length 2M(q). For q ∈ Q, we define an integer S⁺(q) such that the vector (K(q),M(q),S⁺(q)) determines the graph P (if P is...
Equienergetic graphs
Equienergetic self-complementary graphs
In this paper equienergetic self-complementary graphs on vertices for every , and , are constructed.
Equilateral triangles in finite metric spaces.
Équilibre d'un graphe. Quelques résultats algébriques
Équilibre, équivalence, ordre et préordre à distance minimum d'un graphe complet
Les problèmes que nous traitons ici sont en partie familiers aux lecteurs de la revue. L'apport original consiste selon nous dans le fait d'avoir rapproché des problèmes classiques (équilibre d'un graphe, ordre à distance minimum) pour en souligner les analogies profondes et, du coup, plonger de manière féconde ces problèmes dans un ensemble plus large, en particulier en posant le problème de l'équivalence et du préordre à distance minimum d'un graphe complet. Notre exposé se présente donc comme...
Equipped graphs and modular lattices attached to them
Equitable colorations of graphs
Equitable coloring of Kneser graphs
The Kneser graph K(n,k) is the graph whose vertices correspond to k-element subsets of set {1,2,...,n} and two vertices are adjacent if and only if they represent disjoint subsets. In this paper we study the problem of equitable coloring of Kneser graphs, namely, we establish the equitable chromatic number for graphs K(n,2) and K(n,3). In addition, for sufficiently large n, a tight upper bound on equitable chromatic number of graph K(n,k) is given. Finally, the cases of K(2k,k) and K(2k+1,k) are...
Equitable coloring on total graph of bigraphs and central graph of cycles and paths.