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The undirected optical indices of trees

Author

Listed:
  • 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)

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)

Suggested Citation

  • Yuan-Hsun Lo & Hung-Lin Fu & Yijin Zhang & Wing Shing Wong, 2025. "The undirected optical indices of trees," Journal of Combinatorial Optimization, Springer, vol. 49(2), pages 1-22, March.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:2:d:10.1007_s10878-024-01255-2
    DOI: 10.1007/s10878-024-01255-2
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