An edge e of a k-connected graph G is said to be a removable edge if G e is still kconnected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in ...An edge e of a k-connected graph G is said to be a removable edge if G e is still kconnected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in G - e, say x, delete x, and then add edges between any pair of non-adjacent vertices in NG-e(x). The existence of removable edges of k-connected graphs and some properties of 3-connected graphs and 4-connected graphs have been investigated. In the present paper, we investigate some properties of k-connected graphs and study the distribution of removable edges on a cycle in a k-connected graph (k ≥ 4).展开更多
An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G O e denotes the graph obtained from G by the following way: deleting e to get G - e, and for any end vertex of ...An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G O e denotes the graph obtained from G by the following way: deleting e to get G - e, and for any end vertex of e with degree k - 1 in G - e, say x, deleting x, and then adding edges between any pair of non-adjacent vertices in NG-e (x). The existence of removable edges of k-connected graphs and some properties of k-connected graphs have been investigated. In the present paper, we investigate the distribution of removable edges on a spanning tree of a k-connected graph (k ≥ 4).展开更多
An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 i...An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in G- e, say x, delete x, and then add edges between any pair of non-adjacent vertices in NG-e (x). The existence of removable edges of k-connected graphs and some properties of 3-connected and 4-connected graphs have been investigated [1, 11, 14, 15]. In the present paper, we investigate some properties of 5-connected graphs and study the distribution of removable edges on a cycle and a spanning tree in a 5- connected graph. Based on the properties, we proved that for a 5-connected graph G of order at least 10, if the edge-vertex-atom of G contains at least three vertices, then G has at least (3│G│ + 2)/2 removable edges.展开更多
There are various phenomena of malicious information spreading in the real society, which cause many negative impacts on the society. In order to better control the spreading, it is crucial to reveal the influence of ...There are various phenomena of malicious information spreading in the real society, which cause many negative impacts on the society. In order to better control the spreading, it is crucial to reveal the influence of network structure on network spreading. Motifs, as fundamental structures within a network, play a significant role in spreading. Therefore, it is of interest to investigate the influence of the structural characteristics of basic network motifs on spreading dynamics.Considering the edges of the basic network motifs in an undirected network correspond to different tie ranges, two edge removal strategies are proposed, short ties priority removal strategy and long ties priority removal strategy. The tie range represents the second shortest path length between two connected nodes. The study focuses on analyzing how the proposed strategies impact network spreading and network structure, as well as examining the influence of network structure on network spreading. Our findings indicate that the long ties priority removal strategy is most effective in controlling network spreading, especially in terms of spread range and spread velocity. In terms of network structure, the clustering coefficient and the diameter of network also have an effect on the network spreading, and the triangular structure as an important motif structure effectively inhibits the spreading.展开更多
基金Supported by the Science-technology Foundation for Young Scientists of Fujian Province (Grant No. 2007F3070) and National Natural Science Foundation of China (Grant No. 10831001)
文摘An edge e of a k-connected graph G is said to be a removable edge if G e is still kconnected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in G - e, say x, delete x, and then add edges between any pair of non-adjacent vertices in NG-e(x). The existence of removable edges of k-connected graphs and some properties of 3-connected graphs and 4-connected graphs have been investigated. In the present paper, we investigate some properties of k-connected graphs and study the distribution of removable edges on a cycle in a k-connected graph (k ≥ 4).
基金Supported by the National Natural Science Foundation of China(No.11171134)the Fujian Province Science Foundation(No.2013J01014,2011J01015,2007F3070)
文摘An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G O e denotes the graph obtained from G by the following way: deleting e to get G - e, and for any end vertex of e with degree k - 1 in G - e, say x, deleting x, and then adding edges between any pair of non-adjacent vertices in NG-e (x). The existence of removable edges of k-connected graphs and some properties of k-connected graphs have been investigated. In the present paper, we investigate the distribution of removable edges on a spanning tree of a k-connected graph (k ≥ 4).
基金Supported by the National Natural Science Foundation of China (Grant No.10831001)the Science-TechnologyFoundation for Young Scientists of Fujian Province (Grant No.2007F3070)
文摘An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in G- e, say x, delete x, and then add edges between any pair of non-adjacent vertices in NG-e (x). The existence of removable edges of k-connected graphs and some properties of 3-connected and 4-connected graphs have been investigated [1, 11, 14, 15]. In the present paper, we investigate some properties of 5-connected graphs and study the distribution of removable edges on a cycle and a spanning tree in a 5- connected graph. Based on the properties, we proved that for a 5-connected graph G of order at least 10, if the edge-vertex-atom of G contains at least three vertices, then G has at least (3│G│ + 2)/2 removable edges.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62373197 and 62203229)the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX24_1211)。
文摘There are various phenomena of malicious information spreading in the real society, which cause many negative impacts on the society. In order to better control the spreading, it is crucial to reveal the influence of network structure on network spreading. Motifs, as fundamental structures within a network, play a significant role in spreading. Therefore, it is of interest to investigate the influence of the structural characteristics of basic network motifs on spreading dynamics.Considering the edges of the basic network motifs in an undirected network correspond to different tie ranges, two edge removal strategies are proposed, short ties priority removal strategy and long ties priority removal strategy. The tie range represents the second shortest path length between two connected nodes. The study focuses on analyzing how the proposed strategies impact network spreading and network structure, as well as examining the influence of network structure on network spreading. Our findings indicate that the long ties priority removal strategy is most effective in controlling network spreading, especially in terms of spread range and spread velocity. In terms of network structure, the clustering coefficient and the diameter of network also have an effect on the network spreading, and the triangular structure as an important motif structure effectively inhibits the spreading.