Abstract:
A matching $M$ of a graph $G$ is called semistrong, if every edge of $M$ has a vertex of degree one in the induced subgraph by the vertices of $M$. A semistrong edge-coloring of a graph $G$ is a proper edge-coloring in which every color class induces a semistrong matching. The minimum number of colors required for a semistrong edge-coloring is called the semistrong chromatic index of $G$ and denoted by $\chi'_{ss}(G)$. In this paper, we propose a new approach for constructing semistrong edge-colorings and provide an upper bound on the semistrong chromatic index of outerplanar graphs.
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