Let G be a simple connected graph with n vertices.The transmission Tv of a vertex v is defined to be the sum of the distances from v to all other vertices in G,that is,T_(v)=Σ_(u)∈Vd_(uv),where duv denotes the dista...Let G be a simple connected graph with n vertices.The transmission Tv of a vertex v is defined to be the sum of the distances from v to all other vertices in G,that is,T_(v)=Σ_(u)∈Vd_(uv),where duv denotes the distance between u and v.Let T_(1),…,T_(n)be the transmission sequence of G.Let D=(dij)_(n×n)be the distance matrix of G,and T be the transmission diagonal matrix diag(T_(1),…,T_(n)).The matrix Q(G)=T+D is called the distance signless Laplacian of G.In this paper,we provide the distance signless Laplacian spectrum of complete k-partite graph,and give some sharp lower and upper bounds on the distance signless Laplacian spectral radius q(G).展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11801144,11701148)the Natural Science Foundation of Education Ministry of Henan Province(18B110005).
文摘Let G be a simple connected graph with n vertices.The transmission Tv of a vertex v is defined to be the sum of the distances from v to all other vertices in G,that is,T_(v)=Σ_(u)∈Vd_(uv),where duv denotes the distance between u and v.Let T_(1),…,T_(n)be the transmission sequence of G.Let D=(dij)_(n×n)be the distance matrix of G,and T be the transmission diagonal matrix diag(T_(1),…,T_(n)).The matrix Q(G)=T+D is called the distance signless Laplacian of G.In this paper,we provide the distance signless Laplacian spectrum of complete k-partite graph,and give some sharp lower and upper bounds on the distance signless Laplacian spectral radius q(G).
