[PDF] Top 20 Some Extremal Problems in Weighted Graphs

... Graph theory has now become a major branch of applied mathematics and generally regarded as a branch of Combinatorics. Graph theory is a widely used tool for solving a combinatorial problem in different areas such as ... See full document

... coloured graphs which are not complete into monochromatic sub- ...r-edge-coloured graphs of fixed indepen- dence number and bounded the number of monochromatic cycles needed to partition such ...coloured ... See full document

... cactus graphs, and under that name attracted some attention when it was found out that some facility allocation problems that are NP-hard for general graphs can be solved in polynomial ... See full document

... Weighted graphs are as old as that of ...with graphs, especially in networks, weighted graph models are ...tree problems are well ...in weighted graphs. And some ... See full document

... A natural idea we could have would be to store integer approximations of the coor- dinates of all the vertices. This looks like a good idea because it is easy to store integers, and because the function G (n) is easy to ... See full document

... Intersection graphs introduced by Pal [9] also exhibit an important relation between communication system and graph ...of weighted graphs and ...tree problems, strong cycles and paths, all ... See full document

... of some parameter over a collection of ...an extremal problem is when one has a family of objects and a real-valued function on the objects, and one asks for the maximum value attained by the ...in ... See full document

... By a graph G=(V,E) we mean a finite undirected graph without loops or multiple edges. Terms defined here are used in the sense of Harary [1972]. A subset S of V is called a dominating set of G if every vertex not in S is  ... See full document

... control problems of heat equations with a weight ...control problems: one is for equations with multi-domain control under null controllability, and the other is for equations under approximate null ...two ... See full document

... Several authors have studied the problem of obtaining an upper bound for the sum of a domination parameter and a graph theoretic parameter and characterized the corresponding extremal graphs. In [10], ... See full document

... The Jacobi polynomials orthogonal on −1, 1 with respect to the weight function ρx √ 1 − x2 are the so-called Chebyshev polynomials of second kind.. These polynomials are given by Un x.[r] ... See full document

... Throughout this paper we consider only simple and connected graphs. For a graph with vertex set ( ) and edge set ( ). The distance between vertices and in , denoted by ( , ), is the length of a shortest path ... See full document

... a weighted tree automaton (wta), which assigns a weight to each parse ...Under some circumstances, the wta can be determinized, yielding an equivalent, but unambiguous wta, which offers at most one ... See full document

... To establish the main results of this section, we need some preparation. In a polyomino chain, a square having one (respectively two) neighboring square(s) is called terminal (respectively non-terminal). A ... See full document

... Betweenness centrality is a distance-based invariant of graphs. In this paper, we use link and lexicographic products to compute betweenness centrality of some important classes of graphs. Finally, ... See full document

... The paper is laid out as follows. In Section 2, we present some necessary notions and preliminaries, which play an essential role in our proofs. In Section 3, by applying the technique of barrier strips and the ... See full document

... residual graphs was firrst in-duced[1], by ...complete graphs, determined the minimum order of m-Kn-residual graphs are (m+1)n, and (m+1)Kn is the corresponding extremal graph for any ... See full document

... Structure theorems and extremal problems in incidence geometry Hiu Chung Aaron Lin A thesis submitted for the degree of Doctor of Philosophy Department of Mathematics The London School of Economics an[.] ... See full document

... By a classic theorem of Royden [33], any biholomorphism of a finite-type Teich- müller space T g,n is induced a mapping class of the underlying surface S g,n (with some exceptions in low complexity cases). ... See full document

... are extremal among all ...of graphs in terms of their size, and then prove that the eccentric connectivity index grows no faster than a cubic polynomial in the number of ...of graphs for which the ... See full document