Rainbow Neighbourhoods of Graphs
classification
🧮 math.GM
keywords
graphrainbowneighbourhoodconditionestablishexistencegraphsintroduce
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In this paper, we introduce the notion of the rainbow neighbourhood and a related graph parameter namely, the rainbow neighbourhood number of a graph $G$. We report on preliminary results thereof. We also establish a necessary and sufficient condition for the existence of a rainbow neighbourhood in the line graph of a graph $G$.
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