What is it about?
A path decomposition of a graph is a collection of its edge disjoint paths whose union is G. The pendant number $\Pi_p$ is the minimum number of end vertices of paths in a path decomposition of $G$. In this paper, we determine the pendant number of corona products and rooted products of paths and cycles and obtain some bounds for the pendant number for some specifically derived graphs. Further, for any natural number $n$, the existence of a connected graph with pendant number $n$ has also been established. A path decomposition of a graph is a collection of its edge disjoint paths whose union is $G$. The pendant number $\Pi_p$ is the minimum number of end vertices of paths in a path decomposition of $G$. In this paper, we determine the pendant number of corona products and rooted products of paths and cycles and obtain some bounds for the pendant number for some specifically derived graphs. Further, for any natural number $n$, the existence of a connected graph with pendant number $n$ has also been established.
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Why is it important?
The finding it helps us to minimise the entry points and exit points of certain kinds of transportations.
Perspectives
It is a new parameter for graphs recently introduced by our team. It was a great chance for me to work with the above co-authors. The pendant number has a lot of wonderful peculiarities. It is just a beginning and anybody read it can find a lot of thought-provoking insights for further work.
Jomon Sebastian
Read the Original
This page is a summary of: A study on the pendant number of graph products, Acta Universitatis Sapientiae Informatica, August 2019, De Gruyter,
DOI: 10.2478/ausi-2019-0002.
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