[PDF] Top 20 The bounds of crossing number in complete bipartite graphs

... Abstract—We compare the lower bound of crossing number of bipartite and complete bipartite graph with Zarankiewicz conjecture and we illustrate the possible upper bound by a modified Zar[r] ... See full document

... large number of ...forcing number of a graph is NP-hard [9], it is difficult to ...triangle-free graphs in the Wolfram database with between 9 and 22 ...these graphs, the conjecture is ... See full document

... In this paper we consider simple, connected and bipartite graphs. All notations and definitions not given here can be found in [1, 3]. A graph is an ordered pair G = ( V ( G ) , E ( G )) , where V ( G ) is ... See full document

... diameter of G is the greatest distance in G and will be denoted by * . The number of pairs of vertices of G that are distance k is denoted by ( , + . Distance is an important concept in graph theory and it has ... See full document

... of bipartite graphs. The restriction to bipartite graphs is important on its own right and the problem remains quite challenging even under this ...of bipartite graphs defined by ... See full document

... of graphs, e.g., vertex-transitive graphs [] and generalized de Bruijn graphs ...the number of walks and closed walks starting at a given ...upper bounds for the number of ... See full document

... 5. Cvetkovi´c, D, Rowlinson, P: The largest eigenvalue of a graph: a survey. Linear Multilinear Algebra 28, 3-33 (1990) 6. Das, KC, Kumar, P: Bounds on the greatest eigenvalue of graphs. Indian J. Pure ... See full document

... difference graphs similar to sum graphs and similar works we refer [8, ...difference graphs (paths, trees, cycles, special wheels, com- plete graphs, complete bipartite ... See full document

... the number of connected components after removing S from ...a complete graph so that wG − S is always equal to 1, then tG is set to be ...a number of conjectures in 2, including the famous 2-tough ... See full document

... to be either 61 or 62, with a proof of 62 finally arriving in 2000 [4]. Below are pictures of the graph in two forms, one symmetric, the other with minimal crossings. Due to the tediousness of counting that many ... See full document

... bondage number of G, denoted by b(G), is the minimum cardinality of a set of edges B ⊆ E(G) such that γ(G− B) > γ(G), where V (G − B ) = V (G) and E(G − B) = E(G)\B ...bondage number b(G) measures ... See full document

... Abstract. In a graph G , a spanning tree T is said to be a tree t-spanner of the graph G if the distance between any two vertices in T is at most t times their distance in G . The tree t-spanner has many applications in ... See full document

... upper bounds for the number of spanning trees of graphs in terms of the number of vertices, the number of edges and the vertex degrees of ...upper bounds is always better than ... See full document

... vertex-disjoint graphs G and H, the Cartesian product of graphs G and H , denoted by G × H, is a graph such that the vertex set of G × H is the Cartesian product V (G) × V (H ) and any two vertices (u, v) ... See full document

... Of particular interest to us in this thesis is that computing the number of acyclic ori- entations of a graph is the valuation of the chromatic polynomial χ(G, k) of a graph G at k = −1. Computing the chromatic ... See full document

... plication to Algorithms and Computer Science. John Wiley and Sons, New York, 282-300. [3] Fink, J.F. and Jacobson, M.S. (1985) On n-Domination, n-Dependence and Forbidden Sub- graphs. In: Graph Theory with ... See full document

... from complete graphs to complete q-partite ...a complete q-partite graph if G is q-partite with every possible edge between vertices in different ... See full document

... of graphs G and H is the graph with vertex set V(G) V(H) × and edge set is ( , )( , ) u a v b ∈ E G H ( × ) if and only if uv ∈ E G ( ) and ab ∈ E H ( ) ...two graphs G and H is the graph G ⋈ H with ... See full document

... G. The nullity of a graph is the nullity of its adjacency matrix and we use null(G) for the nullity of graph G. If Γ is a signed graph, then ϕ(Γ, λ) is the characteristic polynomial of A(Γ) which referred to as the ... See full document

... graceful graphs is a generalization of the article ...graceful graphs, ...of graphs, including complete graphs and complete bipartite ... See full document