Computing with graphs and groups
نویسنده
چکیده
In this chapter we discuss the computational study of graphs with groups acting on them, and demonstrate various ways in which computational group theoretical methods are used in the study of graphs and groups. We place particular emphasis on the ideas and methods behind the GRAPE and nauty computer packages.
منابع مشابه
Applications of some Graph Operations in Computing some Invariants of Chemical Graphs
In this paper, we first collect the earlier results about some graph operations and then we present applications of these results in working with chemical graphs.
متن کاملComputing Wiener and hyper–Wiener indices of unitary Cayley graphs
The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.
متن کاملComputing Szeged index of graphs on triples
ABSTRACT Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The Szeged index of G is defined by where respectively is the number of vertices of G closer to u (respectively v) than v (respectively u). If S is a set of size let V be the set of all subsets of S of size 3. Then we define t...
متن کاملComputing PI and Hyper–Wiener Indices of Corona Product of some Graphs
Let G and H be two graphs. The corona product G o H is obtained by taking one copy of G and |V(G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, i = 1, 2, …, |V(G)|. In this paper, we compute PI and hyper–Wiener indices of the corona product of graphs.
متن کاملSplice Graphs and their Vertex-Degree-Based Invariants
Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.
متن کاملComputing the First and Third Zagreb Polynomials of Cartesian Product of Graphs
Let G be a graph. The first Zagreb polynomial M1(G, x) and the third Zagreb polynomial M3(G, x) of the graph G are defined as: ( ) ( , ) [ ] e uv E G G x x d(u) + d(v) M1 , ( , ) euvE(G) G x x|d(u) - d(v)| M3 . In this paper, we compute the first and third Zagreb polynomials of Cartesian product of two graphs and a type of dendrimers.
متن کامل