Sucient Conditions for a Graph to Be Super 3-restricted Connected with Given Girth
|Keywords||λ3- optimal Diameter Girth Super restricted connectivity Three restricted edge connectivity|
Many networks, such as transport networks, road networks , electricity networks, communication networks and service network and so can be modeled as Fig . Research network reliability ( some parts of the network failure can still work capacity ) increasingly the more people pay attention to traditional connectivity has its obvious flaws , To this end, it is proposed the concept of a higher level of connectivity , such as super - κm super - λm , m - restrictive point ( edge) connectivity and so on, where m is an integer . This paper studies a general map super - κ3 the λ3 -optimal , super- λ3 . chapter , we introduce the research background and conceptual terms , the study of the history and the various types of connectivity problems a certain extent, an overview of the current situation and the second chapter , the main research the λ3- optimal sufficient condition given the girth chart , proved girth g ≥ 7 the λ3- connected graph minimum degree δ ≥ 3 G , if the diameter D ≤ g ? 3, then G is the λ3- optimal , and on this basis , of diameter D = g ? 2 , G is the λ3- optimal sufficient condition . third chapter , we given girth chart super three restricted connectivity (super-κ3) a sufficient condition to prove that the girth g ≥ 7 minimum degree δ ≥ 3 connected graph G, if the diameter D ≤ g ? , then G is super-κ3 , and prove that if the diameter D ≤ g ? 4 , then G is super-λ3 .