#### Document Type

Conference Proceeding

#### Publication Date

2020

#### Abstract

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*(3*s*, *k*), *GP*(*m*, 2), and *GP*(4*s*, *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.

#### Recommended Citation

Tolentino, J. D., Marcelo, R. M., & Tolentino, M. A. C. (2020, May). Twin chromatic indices of some graphs with maximum degree 3. In Journal of Physics: Conference Series (Vol. 1538, No. 1, p. 012004). IOP Publishing.