supported by the National Natural Science Foundation of China(No.12071351,11571258).
A majority coloring of a directed graph is a vertex-coloring in which every vertex has the same color as at most half of its out-neighbors.Kreutzer et al.conjectured that every digraph is majority 3-colorable.For an i...
Supported by the National Natural Science Foundation of China (Grant No.12001434);The Natural Science Basic Research Program of Shaanxi Province (Grant No.2022JM-006);Chinese Universities Scientific Fund (Grant No.2452020021)
Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix...
supported in part by the National Natural Science Foundation of China(62203352,U2003110);in part by the Key Laboratory Project of Shaanxi Provincial Department of Education(20JS110);in part by the Thousand Talents Plan of Shaanxi Province for Young Professionals。
Maximizing the utilization of lithium-ion battery capacity is an important means to alleviate the range anxiety of electric vehicles.Battery pack inconsistency is the main limiting factor for improving battery pack ca...
REN Shi-quan is supported by China Postdoctoral Science Foundation(Grant No.2022M721023);WANG Chong is supported by Science and Technology Project of Hebei Education Department(Grant No.ZD2022168);Project of Cangzhou Normal University(Grant No.XNJJLYB2021006).
In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic tors...
Supported by the National Natural Science Foundation of China(Grant Nos.11761071,11861068);Guizhou Key Laboratory of Big Data Statistical Analysis,China(Grant No.[2019]5103);the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant No.2022D01E13)。
A jump digraph J(D)of a directed multigraph D has as its vertex set being A(D),the set of arcs of D;where(a,b)is an arc of J(D)if and only if there are vertices u1,v1,u2,v2in D such that a=(u1,v1),b=(u2,v2)and v1≠u2....
supported by the National Natural Science Foundation of China under Grant Nos.61573288,12071370,U1803263,71973103;Key Programs in Shaanxi Province of China under Grant No.2021JZ-12。
In 2011,Liu,et al.investigated the structural controllability of directed networks.They proved that the minimum number of input signals,driver nodes,can be determined by seeking a maximum matching in the directed netw...
Let D be a digraph. A subset S of V (D) is a stable set if every pair of vertices in S is non-adjacent in D. A collection of disjoint paths is a path partition of D, if every vertex in V (D) is in exactly one path of ...
Supported by Science and Technology Project of Hebei Education Department(ZD2022168);Project of Cangzhou Normal University(XNJJLYB2021006);Science and Technology Project of Hebei Education Department(ZD2020410)
For given two digraphs,we can construct a larger digraph through join.The two digraphs that make up the join are called the factors of the join.In this paper,we give a necessary and sufficient condition that the funct...
Let m,t,r and k_(i)(1≤i≤m)be positive integers with k_(i)≥(t+3)r/2,and G be a digraph with vertex set V(G)and arc set E(G).Let H_(1),H_(2),…,H_(t) be t vertex-disjoint subdigraphs of G with mr arcs.In this article...
Supported by the National Natural Science Foundation of China(Grant No.12071351);the Natural Science Foundation of Shandong Provence(Grant No.ZR2020MA043).
A majority k-coloring of a digraph D with k colors is an assignment c:V(D)→{1,2,…,k},such that for every v∈V(D),we have c(w)=c(v)for at most half of all out-neighbors w∈N^(+)(v).For a natural number k≥2,a 1/k-maj...