### Edge-Chromatic Numbers of Glued Graphs

#### Abstract

Let $

*G_*1$ and $*G_*2$ be any two graphs. Assume that $*H_*1*\subseteq**G_*1$ and $*H_*2*\subseteq**G_*2$ are connected, not a single vertex and such that $*H_*1*\cong**H_*2$ with an isomorphism*f*. The*glued graph of*$*G_*1$*and*$*G_*2$*at*$*H_*1$*and*$*H_*2$*with respect to f*, denoted by, is the graph that results from combining $*G_*1$ with $*G_*2$ by identifying $*H_*1$ and $*H_*2$ with respect to the isomorphism*f*between $*H_*1$ and $*H_*2$. We give upper bounds of the edge-chromatic numbers of glued graphs; one is in terms of the edge-chromatic numbers of their original graphs where we give a characterization of graphs satisfying its equality. We further obtain a better upper bound of the chromatic numbers of glued graphs when the original graphs are line graphs.### Refbacks

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