Journal
GRAPHS AND COMBINATORICS
Volume 35, Issue 1, Pages 335-351Publisher
SPRINGER JAPAN KK
DOI: 10.1007/s00373-018-1996-3
Keywords
Turan type extremal problem; Spectral counterparts; Linear forest; Spectral radius; Bipartite graph
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Funding
- Joint NSFC-ISF Research Program - National Natural Science Foundation of China
- Israel Science Foundation [11561141001]
- National Natural Science Foundation of China [11531001]
- Weng Hongwu Research Foundation of Peking University [WHW201803]
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The Turan type extremal problems ask to maximize the number of edges over all graphs which do not contain fixed subgraphs. Similarly, their spectral counterparts ask to maximize spectral radius of all graphs which do not contain fixed subgraphs. In this paper, we determine the maximum spectral radius of all graphs without a linear forest as a subgraph and all the extremal graphs. In addition, the maximum number of edges and spectral radius of all bipartite graphs without kP3 as a subgraph are obtained and all the extremal graphs are also determined. Moreover, some relations between Turan type extremal problems and their spectral counterparts are discussed.
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