The undirected optical indices of trees

Yuan-Hsun Lo (), Hung-Lin Fu (), Yijin Zhang () and Wing Shing Wong ()
Additional contact information
Yuan-Hsun Lo: National Pingtung University
Hung-Lin Fu: National Yang Ming Chiao Tung University
Yijin Zhang: Nanjing University of Science and Technology
Wing Shing Wong: The Chinese University of Hong Kong

Journal of Combinatorial Optimization, 2025, vol. 49, issue 2, No 5, 22 pages

Abstract: Abstract For a connected graph G, an instance I is a set of pairs of vertices and a corresponding routing R is a set of paths specified for all vertex-pairs in I. Let $$\mathfrak {R}_I$$ R I be the collection of all routings with respect to I. The undirected optical index of G with respect to I refers to the minimum integer k to guarantee the existence of a mapping $$\phi :R\rightarrow \{1,2,\ldots ,k\}$$ ϕ : R → { 1 , 2 , … , k } , such that $$\phi (P)\ne \phi (P')$$ ϕ ( P ) ≠ ϕ ( P ′ ) if P and $$P'$$ P ′ have common edge(s), over all routings $$R\in \mathfrak {R}_I$$ R ∈ R I . A natural lower bound of the undirected optical index is the edge-forwarding index, which is defined to be the minimum of the maximum edge-load over all possible routings. Let w(G, I) and $$\pi (G,I)$$ π ( G , I ) denote the undirected optical index and edge-forwarding index with respect to I, respectively. In this paper, we derive the inequality $$w(T,I_A)

Keywords: Optical index; Forwarding index; Path-coloring; All-to-all routing; 05C05; 05C15; 05C90 (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-024-01255-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:49:y:2025:i:2:d:10.1007_s10878-024-01255-2

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-024-01255-2

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().