let G be a graph with n vertices and m edge and thickness and outer thickness of G . We establish inequalities; each of which is best possible up to a constant, between pairs of these parameters. In particular, we show. √B. NikfarjamMH. BararjanpourM. Yahaghi...
All graphs considered in this paper are finite, undirected and simple. Let G be a connected graph with n(G) vertices and e(G) edges. The dimension of cycle space of G is defined as c(G)=e(G)−n(G)+1. If c(G)=0 (resp., c(G)=1; c(G)=2), it is called a tree (re...
Let G = (V,E) be a simple graph with n = |V| vertices and m = |E| edges. The first and the second Zagreb index are defined as Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., where du is the degree of vertex u. Professor Pierre ...
Linear and Multilinear Algebra. Ahead of Print... C Chen,H Jing,S Li - 《Linear & Multilinear Algebra》 被引量: 5发表: 2017年 THE RELATIONSHIP BETWEEN THE MINIMAL RANK OF A TREE AND THE RANK-SPREADS OF THE VERTICES AND EDGES Remarks before the Austin Headliners Club, Austin, Texas, ...
In this paper, we establish a relation-theoretic set-valued version of the fixed point result of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007) on metric spaces endowed with an arbitrary binary relation. The results of this paper, generalize and unify the fi...
In this undirected graph, there is an edge betweenaandbif they are relatively prime. > withGraphTheory: > G1≔RelationGraphseq1..25,NumberTheory:-AreCoprime G1≔Graph 1: an undirected graph with 25 vertices and 199 edge(s) ...
1. Introductory remarks and motivation Throughout this paper graphs are finite, simple, connected and undirected (but with an implicit orientation of the edges when appropriate), and groups are finite. Given a graph X we let V(X), E(X), A(X) and AutX be the set of its vertices, edg...
(T ) (9) where the connected, simple graph G with vertices V = {v1, . . . vn−2}, the sum is over all spanning trees T ∈ T (G), the product is over all edges of e ∈ T , and |W (G)|ii denotes the determinant of the matrix without the i-th row and i-th column...
To draw the digraph of a binary relation on a set A, points, vertices, or nodes, representing the elements of A are drawn. Each ordered pair is represented using an arc, a link, or an edge, with its direction indicated by an arrow. A directed graph, also known as digraph, consists ...
A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set {1,2,…,|V(G)|+|E(G)|} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is called an edge-magic labeling of G, and...