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COVERING GRAPHS WITH OPTIMAL COLLECTION OF EDGES
Keywords:
edge cover, edge covering number, spanning path indicatorDOI:
https://doi.org/10.17654/0974165823006Abstract
A collection U of edges of a graph $G$ is an edge cover of $G$ if every vertex in $G$ is incident with an edge in $U$. The minimum cardinality of an edge cover of $G$ is called the edge covering number of $G$. In this paper, we establish some sharp upper bounds for the edge covering number of graphs resulting from the Cartesian product and composition of two connected graphs in terms of the edge covering numbers of the graphs being considered.
Received: December 1, 2022;
Accepted: December 29, 2022;
References
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S. Pemmaraju and S. Skiena, Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, Cambridge, England: Cambridge University Press, 2003, pp. 318.
E. W. Weisstein, Edge Cover, From MathWorld-A Wolfram Web Resource.
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