For 0≤α<1,theα-spectral radius of an r-uniform hypergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,respectively.In th...For 0≤α<1,theα-spectral radius of an r-uniform hypergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,respectively.In this paper,we show the perturbation ofα-spectral radius by contracting an edge.Then we determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with fixed diameter.We also determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.展开更多
In this note we study the general facility location problem with connectivity. We present an O（np2）-time algorithm for the general facility location problem with connectivity on trees. Furthermore,we present an O（n...In this note we study the general facility location problem with connectivity. We present an O（np2）-time algorithm for the general facility location problem with connectivity on trees. Furthermore,we present an O（np）-time algorithm for the general facility location problem with connectivity on equivalent binary trees.展开更多
A set S of vertices in a graph G = （V, E） without isolated vertices is a total outer-connected dominating set （TCDS） of G if S is a total dominating set of G and G[V - S] is connected. The total outer-connected do...A set S of vertices in a graph G = （V, E） without isolated vertices is a total outer-connected dominating set （TCDS） of G if S is a total dominating set of G and G[V - S] is connected. The total outer-connected domination number of G, denoted by γtc（G）, is the minimum cardinality of a TCDS of G. For an arbitrary graph without isolated vertices, we obtain the upper and lower bounds on γtc（G） ＋ γytc（G）, and characterize the extremal graphs achieving these bounds.展开更多
Let F={H_(1),...,H_(k)}(k≥1)be a family of graphs.The Tur´an number of the family F is the maximum number of edges in an n-vertex{H_(1),...,H_(k)}-free graph,denoted by ex(n,F)or ex(n,{H_(1),H_(2),...,H_(k)}).Th...Let F={H_(1),...,H_(k)}(k≥1)be a family of graphs.The Tur´an number of the family F is the maximum number of edges in an n-vertex{H_(1),...,H_(k)}-free graph,denoted by ex(n,F)or ex(n,{H_(1),H_(2),...,H_(k)}).The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different.In this paper we determine the Tur´an number of the family consisting of a blow-up of a cycle and a blow-up of a star in terms of the Tur´an number of the family consisting of a cycle,a star and linear forests with k edges.展开更多
基金Supported by the National Nature Science Foundation of China(Grant Nos.11871329,11971298)。
文摘For 0≤α<1,theα-spectral radius of an r-uniform hypergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,respectively.In this paper,we show the perturbation ofα-spectral radius by contracting an edge.Then we determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with fixed diameter.We also determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.
基金Supported by National Nature Science Foundation of China(Grant Nos.11471210,11571222)
文摘In this note we study the general facility location problem with connectivity. We present an O（np2）-time algorithm for the general facility location problem with connectivity on trees. Furthermore,we present an O（np）-time algorithm for the general facility location problem with connectivity on equivalent binary trees.
基金Supported by National Natural Science Foundation of China （Grant Nos. 60773078, 10971131） and Shanghai Leading Academic Discipline Project （Grant No. S30104） Thank the referees sincerely for all of the helpful suggestions.
文摘A set S of vertices in a graph G = （V, E） without isolated vertices is a total outer-connected dominating set （TCDS） of G if S is a total dominating set of G and G[V - S] is connected. The total outer-connected domination number of G, denoted by γtc（G）, is the minimum cardinality of a TCDS of G. For an arbitrary graph without isolated vertices, we obtain the upper and lower bounds on γtc（G） ＋ γytc（G）, and characterize the extremal graphs achieving these bounds.
基金Supported by the National Nature Science Foundation of China(Grant Nos.11871329,11971298)。
文摘Let F={H_(1),...,H_(k)}(k≥1)be a family of graphs.The Tur´an number of the family F is the maximum number of edges in an n-vertex{H_(1),...,H_(k)}-free graph,denoted by ex(n,F)or ex(n,{H_(1),H_(2),...,H_(k)}).The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different.In this paper we determine the Tur´an number of the family consisting of a blow-up of a cycle and a blow-up of a star in terms of the Tur´an number of the family consisting of a cycle,a star and linear forests with k edges.
