The Forwarding Indices of Graphs -- a Survey
Jun-Ming Xu, Min Xu

TL;DR
This survey reviews recent research on forwarding indices in graphs, which measure maximum load in network routing, highlighting known results, open problems, and conjectures in the field.
Contribution
It compiles and discusses existing results, open problems, and conjectures related to forwarding indices in graphs, providing a comprehensive overview of the topic.
Findings
Summarizes key results on vertex and edge forwarding indices.
Identifies open problems and conjectures in the field.
Highlights the importance of minimizing forwarding indices for network efficiency.
Abstract
A routing of a given connected graph of order is a collection of simple paths connecting every ordered pair of vertices of . The vertex-forwarding index of with respect to is defined as the maximum number of paths in passing through any vertex of . The vertex-forwarding index of is defined as the minimum over all routing 's of . Similarly, the edge-forwarding index of with respect to is the maximum number of paths in passing through any edge of . The edge-forwarding index of is the minimum over all routing 's of . The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention in the past ten years…
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Graph theory and applications
