In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission...In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission rate of Downlink Users(DUs).Meanwhile,the Quality of Service(QoS)of all D2D users must be satisfied.We comprehensively considered the interference among D2D communications and downlink transmissions.The original problem is strongly non-convex,which requires high computational complexity for traditional optimization methods.And to make matters worse,the results are not necessarily globally optimal.In this paper,we propose a novel Graph Neural Networks(GNN)based approach that can map the considered system into a specific graph structure and achieve the optimal solution in a low complexity manner.Particularly,we first construct a GNN-based model for the proposed network,in which the transmission links and interference links are formulated as vertexes and edges,respectively.Then,by taking the channel state information and the coordinates of ground users as the inputs,as well as the location of UAVs and the transmission power of all transmitters as outputs,we obtain the mapping from inputs to outputs through training the parameters of GNN.Simulation results verified that the way to maximize the total transmission rate of DUs can be extracted effectively via the training on samples.Moreover,it also shows that the performance of proposed GNN-based method is better than that of traditional means.展开更多
A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set ...A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set of G. In this paper we calculate the k-domination number (for k = 2) of the product of two paths Pm × Pn for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].展开更多
BACKGROUND Gastric cancer is a leading cause of cancer-related deaths worldwide.Prognostic assessments are typically based on the tumor-node-metastasis(TNM)staging system,which does not account for the molecular heter...BACKGROUND Gastric cancer is a leading cause of cancer-related deaths worldwide.Prognostic assessments are typically based on the tumor-node-metastasis(TNM)staging system,which does not account for the molecular heterogeneity of this disease.LATS2,a tumor suppressor gene involved in the Hippo signaling pathway,has been identified as a potential prognostic biomarker in gastric cancer.AIM To construct and validate a nomogram model that includes LATS2 expression to predict the survival prognosis of advanced gastric cancer patients following ra-dical surgery,and compare its predictive performance with traditional TNM staging.METHODS A retrospective analysis of 245 advanced gastric cancer patients from the Fourth Hospital of Hebei Medical University was conducted.The patients were divided into a training group(171 patients)and a validation group(74 patients)to deve-lop and test our prognostic model.The performance of the model was determined using C-indices,receiver operating characteristic curves,calibration plots,and decision curves.RESULTS The model demonstrated a high predictive accuracy with C-indices of 0.829 in the training set and 0.862 in the validation set.Area under the curve values for three-year and five-year survival prediction were significantly robust,suggesting an excellent discrimination ability.Calibration plots confirmed the high concordance between the predictions and actual survival outcomes.CONCLUSION We developed a nomogram model incorporating LATS2 expression,which significantly outperformed conven-tional TNM staging in predicting the prognosis of advanced gastric cancer patients postsurgery.This model may serve as a valuable tool for individualized patient management,allowing for more accurate stratification and im-proved clinical outcomes.Further validation in larger patient cohorts will be necessary to establish its generaliza-bility and clinical utility.展开更多
Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological in...Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J<sub>2,m</sub> for all integer number m ≥ 3 are calculated.展开更多
In this paper we prove that the join of two path graphs, two cycle graphs, Ladder graph and the tensor product are H2-cordial labeling. Further we prove that the join of two wheel graphs Wn and Wm, (mod 4) admits a H-...In this paper we prove that the join of two path graphs, two cycle graphs, Ladder graph and the tensor product are H2-cordial labeling. Further we prove that the join of two wheel graphs Wn and Wm, (mod 4) admits a H-cordial labeling.展开更多
In this study, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on weighted graphs. Then, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on i...In this study, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on weighted graphs. Then, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on interval weighted graphs. Their behaviors are investigated under some graph operations by using these definitions.展开更多
A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this pape...A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this paper, we show that for or 11, which confirms Conjecture 6.1 stated in [X. Li, V. Mak-Hau, S. Zhou, The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups, J. Comb. Optim. (2013) 25: 716-736] in the case when or 11. Moreover, we show that? if 1) either (mod 6), m is odd, r = 3, or 2) (mod 3), m is even (mod 2), r = 0.展开更多
如果 S 是一个统治集合，导致的 subgraph 至多有 k 部件， V 的子集 S 被称为一个连接 k 的统治集合。G 的连接 k 的支配数字 kc (G) 是在 G 的所有最小的连接 k 的统治集合上拿的最小的集的势。在这份报纸，我们与相等的连接支配和 2-...如果 S 是一个统治集合，导致的 subgraph 至多有 k 部件， V 的子集 S 被称为一个连接 k 的统治集合。G 的连接 k 的支配数字 kc (G) 是在 G 的所有最小的连接 k 的统治集合上拿的最小的集的势。在这份报纸，我们与相等的连接支配和 2-connected 支配数字描绘树和 unicyclic 图。展开更多
For a given graph H, a graphic sequence π =(d1, d2, ···, dn) is said to be potentially H-graphic if π has a realization containing H as a subgraph. In this paper, we characterize the potentially C6+ P...For a given graph H, a graphic sequence π =(d1, d2, ···, dn) is said to be potentially H-graphic if π has a realization containing H as a subgraph. In this paper, we characterize the potentially C6+ P2-graphic sequences where C6+ P2 denotes the graph obtained from C6 by adding two adjacent edges to the three pairwise nonadjacent vertices of C6. Moreover, we use the characterization to determine the value of σ(C6+ P2, n).展开更多
基金supported in part by the National Natural Science Foundation of China(61901231)in part by the National Natural Science Foundation of China(61971238)+3 种基金in part by the Natural Science Foundation of Jiangsu Province of China(BK20180757)in part by the open project of the Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space,Ministry of Industry and Information Technology(KF20202102)in part by the China Postdoctoral Science Foundation under Grant(2020M671480)in part by the Jiangsu Planned Projects for Postdoctoral Research Funds(2020z295).
文摘In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission rate of Downlink Users(DUs).Meanwhile,the Quality of Service(QoS)of all D2D users must be satisfied.We comprehensively considered the interference among D2D communications and downlink transmissions.The original problem is strongly non-convex,which requires high computational complexity for traditional optimization methods.And to make matters worse,the results are not necessarily globally optimal.In this paper,we propose a novel Graph Neural Networks(GNN)based approach that can map the considered system into a specific graph structure and achieve the optimal solution in a low complexity manner.Particularly,we first construct a GNN-based model for the proposed network,in which the transmission links and interference links are formulated as vertexes and edges,respectively.Then,by taking the channel state information and the coordinates of ground users as the inputs,as well as the location of UAVs and the transmission power of all transmitters as outputs,we obtain the mapping from inputs to outputs through training the parameters of GNN.Simulation results verified that the way to maximize the total transmission rate of DUs can be extracted effectively via the training on samples.Moreover,it also shows that the performance of proposed GNN-based method is better than that of traditional means.
文摘A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set of G. In this paper we calculate the k-domination number (for k = 2) of the product of two paths Pm × Pn for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].
文摘BACKGROUND Gastric cancer is a leading cause of cancer-related deaths worldwide.Prognostic assessments are typically based on the tumor-node-metastasis(TNM)staging system,which does not account for the molecular heterogeneity of this disease.LATS2,a tumor suppressor gene involved in the Hippo signaling pathway,has been identified as a potential prognostic biomarker in gastric cancer.AIM To construct and validate a nomogram model that includes LATS2 expression to predict the survival prognosis of advanced gastric cancer patients following ra-dical surgery,and compare its predictive performance with traditional TNM staging.METHODS A retrospective analysis of 245 advanced gastric cancer patients from the Fourth Hospital of Hebei Medical University was conducted.The patients were divided into a training group(171 patients)and a validation group(74 patients)to deve-lop and test our prognostic model.The performance of the model was determined using C-indices,receiver operating characteristic curves,calibration plots,and decision curves.RESULTS The model demonstrated a high predictive accuracy with C-indices of 0.829 in the training set and 0.862 in the validation set.Area under the curve values for three-year and five-year survival prediction were significantly robust,suggesting an excellent discrimination ability.Calibration plots confirmed the high concordance between the predictions and actual survival outcomes.CONCLUSION We developed a nomogram model incorporating LATS2 expression,which significantly outperformed conven-tional TNM staging in predicting the prognosis of advanced gastric cancer patients postsurgery.This model may serve as a valuable tool for individualized patient management,allowing for more accurate stratification and im-proved clinical outcomes.Further validation in larger patient cohorts will be necessary to establish its generaliza-bility and clinical utility.
文摘Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J<sub>2,m</sub> for all integer number m ≥ 3 are calculated.
文摘In this paper we prove that the join of two path graphs, two cycle graphs, Ladder graph and the tensor product are H2-cordial labeling. Further we prove that the join of two wheel graphs Wn and Wm, (mod 4) admits a H-cordial labeling.
文摘In this study, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on weighted graphs. Then, the SK, SK<sub>1</sub> and SK<sub>2</sub> indices are defined on interval weighted graphs. Their behaviors are investigated under some graph operations by using these definitions.
文摘A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this paper, we show that for or 11, which confirms Conjecture 6.1 stated in [X. Li, V. Mak-Hau, S. Zhou, The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups, J. Comb. Optim. (2013) 25: 716-736] in the case when or 11. Moreover, we show that? if 1) either (mod 6), m is odd, r = 3, or 2) (mod 3), m is even (mod 2), r = 0.
文摘如果 S 是一个统治集合，导致的 subgraph 至多有 k 部件， V 的子集 S 被称为一个连接 k 的统治集合。G 的连接 k 的支配数字 kc (G) 是在 G 的所有最小的连接 k 的统治集合上拿的最小的集的势。在这份报纸，我们与相等的连接支配和 2-connected 支配数字描绘树和 unicyclic 图。
基金Foundation item： Supported by the National Natural Science Foundation of China（11101358） Supported by the Project of Fujian Education Department（JA11165）+1 种基金 Supported by the Project of Education Department of Fujian Province（JA12209） Supported by the Project of Zhangzhou Teacher＇s College（S11104）
文摘For a given graph H, a graphic sequence π =(d1, d2, ···, dn) is said to be potentially H-graphic if π has a realization containing H as a subgraph. In this paper, we characterize the potentially C6+ P2-graphic sequences where C6+ P2 denotes the graph obtained from C6 by adding two adjacent edges to the three pairwise nonadjacent vertices of C6. Moreover, we use the characterization to determine the value of σ(C6+ P2, n).
基金supported by National Natural Science Foundation of the People’s Republic of China“On the symmetries and local properties of graphs with square-free order”(11601005)Anhui Provincial Science Fund for Excellent Young Scholars“On the symmetries of edge-primitive graphs with square-free order”(gxyq2020011).
