Graph Compositions I: Basic Enumeration
نویسندگان
چکیده
The idea of graph compositions generalizes both ordinary compositions of positive integers and partitions of finite sets. In this paper we develop formulas, generating functions, and recurrence relations for composition counting functions for several families of graphs.
منابع مشابه
A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$. In this case, $B$ is called a textit{metric basis} for $G$. The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$. Givi...
متن کاملFibonacci Polytopes and Their Applications
A Fibonacci d-polytope of order k is defined as the convex hull of {0, 1}-vectors with d entries and no consecutive k ones, where k ≤ d. We show that these vertices can be partitioned into k subsets such that the convex hull of the subsets give the equivalent of Fibonacci (d− i)polytopes, for i = 1, . . . , k, which yields a “Fibonacci like” recursive formula to enumerate the vertices. Surprisi...
متن کاملInside-Out Polytopes
We present a common generalization of counting lattice points in rational polytopes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an integer whose parts are partially distinct, and generalized latin squares. Our method is to generalize Ehrhart’s theory of lattice-point counting to a convex pol...
متن کاملCoset Enumeration, Permutation Group Algorithms, and Applications to Graphs and Geometries
In these notes we discuss coset enumeration and basic permutation group algorithms. To illustrate some applications to graphs and nite geometries, we classify and study some graphs which are locally the incidence graph of the 2 ? (11; 5; 2) design.
متن کاملCounting l-letter subwords in compositions
Let N be the set of all positive integers and let A be any ordered subset of N. Recently, Heubach and Mansour enumerated the number of compositions of n with m parts in A that contain the subword τ exactly r times, where τ ∈ {111, 112, 221, 123}. Out aims are (1) to generalize the above results, i.e., to enumerate the number of compositions of n with m parts in A that contain an l-letter subwor...
متن کامل