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The Generalized τ-Bases of Primitive Non-Powerful Signed Digraphs with d Loops

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Abstract

Let n, k, τ, d be positive integers with 1 ≤ k, τ, d ≤ n. As natural extensions of the bases, the kth local bases, the kth upper bases and the kth lower bases of primitive non-powerful signed digraphs, we introduce a number of new, though, intimately related parameters called the generalized τ-bases of primitive non-powerful signed digraphs. Moreover, some sharp bounds for the generalized τ-bases of primitive non-powerful signed digraphs with n vertices and d loops are obtained, respectively.

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Authors and Affiliations

  1. School of Mathematical Science, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Yufei Huang, Bolian Liu & Siyuan Chen

Authors
  1. Yufei Huang
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  2. Bolian Liu
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  3. Siyuan Chen
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Corresponding author

Correspondence to Bolian Liu.

Additional information

This work is supported by NNSF of China (No.11071088).

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Huang, Y., Liu, B. & Chen, S. The Generalized τ-Bases of Primitive Non-Powerful Signed Digraphs with d Loops. Graphs and Combinatorics 28, 227–242 (2012). https://doi.org/10.1007/s00373-011-1036-z

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  • DOI: https://doi.org/10.1007/s00373-011-1036-z

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