Abstract
Let be a proper k-edge coloring of a simple connected graph of order at the latest 3, where the set of colors is. If a proper edge coloring of a graph that induces vertex coloring is a proper vertex coloring, then is called a twin edge k-coloring of a graph. the twin chromatic number of a graph is the least value k of colors of a graph, and denote it by. In this paper, we obtains the twin chromatic number of infinite paths and finite paths.
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