Twin chromatic indices of some graphs with maximum degree 3
Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from k and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in k ) of the colors of the edges incident with v. The...
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| Main Authors: | , , |
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| Format: | text |
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Archīum Ateneo
2020
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| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/125 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1124&context=mathematics-faculty-pubs |
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| Institution: | Ateneo De Manila University |
| Summary: | Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from k and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in k ) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by . In this paper, we determine the twin chromatic indices of circulant graphs , and some generalized Petersen graphs such as GP(3s, k), GP(m, 2), and GP(4s, l) where n ≥ 6 and n ≡ 0 (mod 4), s ≥ 1, k ≢ 0 (mod 3), m ≥ 3 and m {4, 5}, and l is odd. Moreover, we provide some sufficient conditions for a connected graph with maximum degree 3 to have twin chromatic index greater than 3. |
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