Graph Operations Characterizing Rank-Width and Balanced Graph Expressions
نویسندگان
چکیده
Graph complexity measures like tree-width, clique-width, NLC-width and rank-width are important because they yield Fixed Parameter Tractable algorithms. Rank-width is based on ranks of adjacency matrices of graphs over GF(2). We propose here algebraic operations on graphs that characterize rank-width. For algorithmic purposes, it is important to represent graphs by balanced terms. We give a unique theorem that generalizes several “balancing theorems” for tree-width and clique-width. New results are obtained for rank-width and a variant of clique-width, called m-clique-width.
منابع مشابه
Graph operations characterizing rank-width
Graph complexity measures like tree-width, clique-width and rank-width are important because they yield Fixed Parameter Tractable algorithms. These algorithms are based on hierarchical decompositions of the considered graphs and on boundedness conditions on the graph operations that, more or less explicitly, recombine the components of decompositions into larger graphs. Rank-width is de ned in ...
متن کاملApplications 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 کاملRemarks on Distance-Balanced Graphs
Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.
متن کاملBalanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...
متن کاملCharacteristics of Common Neighborhood Graph under Graph Operations and on Cayley Graphs
Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...
متن کامل