In a directed Graph ofNnodes andMedges what is the maximum number ofShortest pathsfrom any nodeUto another nodeV? And the same for undirected Graph ? My question came from this problem1321D - Navigation Systemwhere i needed to calculate the number of paths from any node to nodetand didn'...
n, k)-star graphparallel computingWe count the shortest paths, not necessarily disjoint, between any two vertices in an (n, k)-star graph by counting the minimum factorizations of a permutation in terms of the transpositions corresponding to edges in that graph. This result generalizes a ...
Edge betweenness is a measure of the influence of edges in networks. The edge betweenness of an edge is defined to be the number of shortest paths between ... Majstorovic,Caporossi - 《Graphs & Combinatorics》 被引量: 1发表: 2015年 Bounds on the Steiner radius of a graph For a connect...
. In graph theory, the most investigated intervals are geodesic intervals that are built from shortest paths and monophonic intervals arising from induced paths [7]. The geodesic interval IG(u,v) between vertices u and v is the set of all vertices that lie on some shortest path between u ...
In that contest, there was a problem requiring counting the number of shortest paths from a vertex s to every other vertex in a directed weighted graph. I have implemented my idea and tested it a bit so I had a strong belief that my code was correct. In the end, it turned out that...
Let G be a graph with exactly one hole. Then the competition number of G is at most 2. In fact, Kim [8] conjectured that the competition number of a graph with h holes is at most h+1. Li and Chang [11] showed that this conjecture is true for graphs in which all the holes ar...
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aDjikstra's algorithm (named after its discover, E.W. Dijkstra) solves the problem of finding the shortest path from a point in a graph (the source) to a destination. It turns out that one can find the shortest paths from a given source to all points in a graph in the same time, ...
A vertex v of a connected graph G distinguishes a pair u, w of vertices of G if d(v, u)d(v, w), where d(,) denotes the length of a shortest path between two vertices in G. A k-partition ={S-1, S-2, ..., S-k} of the vertex set of G is said to be a locatic pa...
In radio antipodal labeling, the channels were reused again for the antipodal vertices. It will reduce the usage of the number of channels, with minimum interference. Hence it is a better labeling compared to other labelings. It is a mappingτfrom the vertex set of a graphTto the set of ...