Partially supported by National Natural Science Foundation of China(No.11771172);key scientific and technological project of higher education of Henan Province(No.19A110019);Science and technology innovation fund of Henan Agricultural University(No.KJCX2019A15);Partially supported by the Ph D Research Foundation of Henan Agricultural University(No.30500614)
A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote ...
A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and numb...
Let G be a graph, in which each vertex (job) v has a positive integer weight (processing time) p(v) and eachedge (u,v) represented that the pair of jobs u and v cannot be processed in the same slot. In this paper we a...
SuppoSed by the Ministry of Communication(200332922505); the Doctoral Foundation of Ministry of Education(20030151005)
The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a...
Abstract The paper proves that if G is a k tree, then the bandwidth B(G) of the complement G of G is given by B(G)=n-k-1, when GK k+K n-k , n-k-2, otherwise.