Radio k-chromatic number of cycles for large k

Karst, Nathaniel J.; Langowitz, Joshua; Oehrlein, Jessica; Troxell, Denise Sakai

doi:10.1142/s1793830917500318

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…Most results in this paper are extensions of results by Karst, Langowitz, Oehrlein, and Troxell [9], and by Liu and Zhu [14]. The method of using the Φ-function to prove a lower bound for the radio k-number for C n was introduced in [14] when k = n 2 , the diameter of C n .…”

Section: Closing Remarksmentioning

confidence: 93%

“…The method of using the Φ-function to prove a lower bound for the radio k-number for C n was introduced in [14] when k = n 2 , the diameter of C n . The authors proved that rn k (C n ) = LB(n, d) for all n. This method was applied and extended in [9], where the authors completely determined the radio k-number for C n when k = n 2 + 1, the diameter of C n plus one. Theorem 15.…”

Section: Closing Remarksmentioning

confidence: 99%

“…The following proposition from [9] greatly reduces the number of inequalities to verify when determining if a map f is a radio-k-labeling.…”

Section: Preliminary and Notationsmentioning

confidence: 99%

“…Now we turn to the case when k < n − 3 and n ≡ k (mod 2). We begin with a result from Karst, Langowitz, Oehrlein, and Sakai [9]. For completeness we include a proof.…”

Section: Exact Values For Rn K (C N )mentioning

confidence: 99%

“…Also, rn d−1 (C n ) when n ≡ 0 (mod 4) has been determined in [8], where bounds are given for the case when n ≡ 0 (mod 4). Karst, Langowitz, Oehrlein, and Sakai in [9] studied radio-k-labeling when k diam(C n ) and determined the value of…”

Section: Introductionmentioning

confidence: 99%

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Radio-k-Labeling of Cycles for Large k

Bloomfield¹,

Liu²,

Ramirez³

2021

Preprint

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Let G be a simple connected graph. For any two vertices u and v, let d(u, v) denote the distance between u and v in G. A radio-k-labeling of G for a fixed positive integer k is a function f which assigns to each vertex a non-negative integer label such that for every two vertices u and v in G,The span of f is the difference between the largest and smallest labels of f (V ). The radio-k-number of a graph G, denoted by rn k (G), is the smallest span among all radio-k-labelings admitted by G. A cycle Cn has diameter d = n/2 . In this paper, we combine a lower bound approach with algebraic cyclic group structure to determine the value of rn k (Cn) for k n − 3. For d k < n − 3, we obtain the values of rn k (Cn) when n and k have the same parity, and prove partial results when n and k have different parities. Our results extend the known values of rn d (Cn) and rn d+1 (Cn) shown by Liu and Zhu [14], and by Karst, Langowitz, Oehrlein and Troxell [9], respectively.

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Section: Closing Remarksmentioning

confidence: 93%

Section: Closing Remarksmentioning

confidence: 99%

“…The following proposition from [9] greatly reduces the number of inequalities to verify when determining if a map f is a radio-k-labeling.…”

Section: Preliminary and Notationsmentioning

confidence: 99%

“…Now we turn to the case when k < n − 3 and n ≡ k (mod 2). We begin with a result from Karst, Langowitz, Oehrlein, and Sakai [9]. For completeness we include a proof.…”

Section: Exact Values For Rn K (C N )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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