And we consider the special case of b′\-w(G), that b′\-w(G) is equal to 1, we call G is edge-removal-critical(ER-critical). Then give necessary and sufficient condition for regular graphs to be γ\-w-ER-critical and necessary condition for general graph to be γ\-w-ER-critical.
Sufficient and necessary conditions for coverings and deletions of parity ( g,f )_factors of a general graph are given, and their duality is investigated.
In Chaper 2, we present lower and upper bounds on λ_e interms of the maximum degree for general graphs, and show that λ(L(G)) ≤ [(Δ_L~2)/2 +2Δ_L-1] ≤ Δ_L~2, which implies that all line graphs are consistent with the conjecture of Griggs and Yen.
Give the definition of the fissile graph, extend the L(d,1)-labeling of graphs to the L(0,1,2d,d,1)-labeling of weighted graphs, and give an upper bound of the L(0,1,2d,d,1)-labeling number of the fissile graphs for the general graphs and two classes of planar graphs and their correlative graphs.
The first chapter introduces the basic concepts of general graphs, traditional hypergraphs and information hypergraphs, as well as the research development of graph labeling, cycle decomposition of traditional hypergraphs and information hypergraph.
We prove that the time complexity to solve this routing problem over general graph networks is NP-complete, and then propose a routing algorithm for overlay networks to minimize server load.
This paper looks bricfly at the way how to deal with the problem of the travel time from the facility to areas within the graph(that is, collections of points as opposed to individual points). As am extension of the results in[4], we generalize the problem by permitting an optimal point (to he) laid either on an edge or on a vertex of the graph instead of only on a vertex. The cancept of absolute S-center and S-median of a graph G is introduced as follows:
Hoasoya's index is an important index indicating the properties of physics and chemistry of an organic structure in molecular topology, The graphs with single cyele represent a kind of compounds with a single ring. In this.paper, couut formulae of Hosoya's indcx for this type of graphs are given as well as two theorems of Hosoya's index for general graphs.