Twin chromatic indices of some graphs with maximum degree 3
J D Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino · Journal of Physics Conference Series · 2020
Abstract Letk≥ 2 be an integer andGbe a connected graph of order at least 3. A twink-edge coloring ofGis a proper edge coloring ofGthat uses colors from ℤkand that induces a proper vertex coloring onGwhere the color of a vertexvis the sum (in ℤk) of the colors of the edges incident withv. The smallest integerkfor whichGhas a twink-edge coloring is the twin chromatic index ofGand is denoted by χt′(G) . In this paper, we determine the twin chromatic indices of circulant graphs Cn(1,n2) , and some generalized Petersen graphs such asGP(3s,k),GP(m, 2), andGP(4s,l) wheren≥ 6 andn≡ 0 (mod 4),s≥ 1,k≢ 0 (mod 3), m ≥ 3 and m ∉ {4, 5}, andlis odd. Moreover, we provide some sufficient conditions for a connected graph with maximum degree 3 to have twin chromatic index greater than 3.