Gracefully Cultivating Trees on a Cycle
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説明
Abstract A graph G of size q is graceful if there exists an injective function f : V ( G ) → { 0 , 1 , … , q } such that each u v ∈ E ( G ) is labeled | f ( u ) − f ( v ) | and the resulting edge labels are distinct. Truszczynski conjectured that all unicyclic graphs except the cycle C n , where n ≡ 1 or 2 ( mod 4 ) , are graceful. In this paper, we present two methods to construct certain graceful unicyclic graphs when the length of cycles are congruent to 0 or 3 (mod 4).
収録刊行物
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- Electronic Notes in Discrete Mathematics
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Electronic Notes in Discrete Mathematics 48 143-150, 2015-07-01
Elsevier BV