Discrete Mathematics, Algorithms and Applications, Dec 7, 2020
The total chromatic number [Formula: see text] is the least number of colors needed to color the ... more The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text] is the maximum degree of [Formula: see text]. For the powers of cycles, Campos and de Mello proposed the following conjecture: Let [Formula: see text] denote the graphs of powers of cycles of order [Formula: see text] and length [Formula: see text] with [Formula: see text]. Then, [Formula: see text] In this paper, we prove the Campos and de Mello’s conjecture for some classes of powers of cycles. Also, we prove the TCC for complement of powers of cycles.
Asia-Pacific Conference on Communications, Dec 1, 2008
The paper proposes an improved module-based substitution method for image hiding. The method has ... more The paper proposes an improved module-based substitution method for image hiding. The method has the following characteristics: (1) The extracted data are lossless. (2) Each k-bit datum is hidden in a pixel of the host image, and the gray-value distortion is not larger than 2k-1 for most of the pixels. (3) If it is compared with reported lossless Least-Significant-Bits (LSB)
Journal of Discrete Mathematical Sciences and Cryptography, Nov 17, 2017
Abstract Let Gυu denote the graph Kυ\Ku if both u and υ are odd, and (Kυ – F1)\(Ku – F2) if both ... more Abstract Let Gυu denote the graph Kυ\Ku if both u and υ are odd, and (Kυ – F1)\(Ku – F2) if both u and υ are even, where F1 is a 1-factor of Kυ and F2 is a 1-factor of Ku with F2⊆F1. In this paper, we study the existence problem of m-cycle design of Gυu. By using direct and recurssive constructions, we obtain several new m-cycle design of Gυu.
Discrete Mathematics, Algorithms and Applications, Dec 7, 2020
The total chromatic number [Formula: see text] is the least number of colors needed to color the ... more The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text] is the maximum degree of [Formula: see text]. For the powers of cycles, Campos and de Mello proposed the following conjecture: Let [Formula: see text] denote the graphs of powers of cycles of order [Formula: see text] and length [Formula: see text] with [Formula: see text]. Then, [Formula: see text] In this paper, we prove the Campos and de Mello’s conjecture for some classes of powers of cycles. Also, we prove the TCC for complement of powers of cycles.
Asia-Pacific Conference on Communications, Dec 1, 2008
The paper proposes an improved module-based substitution method for image hiding. The method has ... more The paper proposes an improved module-based substitution method for image hiding. The method has the following characteristics: (1) The extracted data are lossless. (2) Each k-bit datum is hidden in a pixel of the host image, and the gray-value distortion is not larger than 2k-1 for most of the pixels. (3) If it is compared with reported lossless Least-Significant-Bits (LSB)
Journal of Discrete Mathematical Sciences and Cryptography, Nov 17, 2017
Abstract Let Gυu denote the graph Kυ\Ku if both u and υ are odd, and (Kυ – F1)\(Ku – F2) if both ... more Abstract Let Gυu denote the graph Kυ\Ku if both u and υ are odd, and (Kυ – F1)\(Ku – F2) if both u and υ are even, where F1 is a 1-factor of Kυ and F2 is a 1-factor of Ku with F2⊆F1. In this paper, we study the existence problem of m-cycle design of Gυu. By using direct and recurssive constructions, we obtain several new m-cycle design of Gυu.
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