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Graphic Sequences with an A-Connected Realization

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Abstract

A non-increasing sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) of non-negative integers is said to be graphic if it is the degree sequence of a simple graph G on n vertices. Let A be an (additive) abelian group. An extremal problem for a graphic sequence to have an A-connected realization is considered as follows: determine the smallest even integer \({\sigma (A, n)}\) such that each graphic sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) with d n ≥ 2 and \({\sigma (\pi) = d_1 + d_2 + \cdots +d_n \ge \sigma (A, n)}\) has an A-connected realization. In this paper, we determine \({\sigma (A, n)}\) for |A| ≥ 5 and n ≥ 3.

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Authors and Affiliations

  1. Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, China

    Jianhua Yin

  2. Department of Mathematics, West Virginia University, Morgantown, WV, 26506-6310, USA

    Rong Luo

  3. Lane Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, WV, 26506, USA

    Guodong Guo

Authors
  1. Jianhua Yin
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  2. Rong Luo
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  3. Guodong Guo
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Corresponding author

Correspondence to Jianhua Yin.

Additional information

J. Yin’s research is partially supported by National Natural Science Foundation of China (Grant No. 11161016).

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Yin, J., Luo, R. & Guo, G. Graphic Sequences with an A-Connected Realization. Graphs and Combinatorics 30, 1615–1620 (2014). https://doi.org/10.1007/s00373-013-1363-3

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  • DOI: https://doi.org/10.1007/s00373-013-1363-3

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