Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Relating path coverings to vertex labellings with a condition at distance two
Discrete Mathematics
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
On L(d, 1)-labelings of graphs
Discrete Mathematics
On generalized Petersen graphs labeled with a condition at distance two
Discrete Mathematics
Distance-two labelings of graphs
European Journal of Combinatorics
Channel Assignment with Separation for Interference Avoidance in Wireless Networks
IEEE Transactions on Parallel and Distributed Systems
On the span in channel assignment problems: bounds, computing and counting
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Graph labeling and radio channel assignment
Journal of Graph Theory
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To reduce the interfering among transmitters, any two 'close'transmitters, with distance no more than d2, mustreceive frequencies at least l2 apart, and any two 'veryclose' transmitters, with distance no more than d1, mustreceive channels at least l1 apart. Theassignment problem is to assign a frequency to each transmittersuch that total bandwidth of assigned frequencies can be minimised.In this paper, we present upper and lower bounds of the minimumbandwidth of cycles and powers of cycles. We also show thecorresponding assignment functions. And then we partially solve theassignment problem of cycles Cn and their powers suchas: (i) 3 ≤ n ≤ 2d1+1; (ii) 2d1 + 2≤ n ≤ 2d2 + 1, q1 ≠ 0 andl1 ≤ m1l2; (iii) 2d1+ 2 ≤ n ≤ 2d2 + 1, q1 ≡ 1(modm1) and l1 m1l2;(iv) 2d1 + 2 ≤ n ≤ 2d2 + 1,q1 = 0 and l1 ≥ (m1 +d1 − 1)l2 or l1 ≤(m1 − 1)l2; (v) n ≥ 2d2 +2 and l1 ≤ ⌊(d2 +⌊q2/m2⌋)/(d1 +1)⌋l2; and (vi) n ≥ 2d2 + 2,q1 ≡ 1(mod m1), and l1 m1l2, where n = mi(di +1) + qi and 0 ≤ qi ≤ di.