Monophonic eccentric domination in graphs

Document Type : Original paper

Authors

1 Department of Mathematics, University College of Engineering Nagercoil, Anna University, Tirunelveli Region, Nagercoil - 629 004, India

2 Department of Mathematics, Scott Christian College (Autonomous), Nagercoil - 629 003, India

Abstract

For any two vertices u and v in a connected graph G, the monophonic distance dm(u,v) from u to v is defined as the length of a longest u−v monophonic path in G. The monophonic eccentricity em(v) of a vertex v in G is the maximum monophonic distance from v to a vertex of G.  A vertex v in G is a monophonic eccentric vertex of a vertex u in G if em(u)=dm(u,v). A set S⊆V  is a  monophonic eccentric  dominating set if every vertex in V−S has a monophonic eccentric vertex in S. The monophonic eccentric  domination number γme(G) is the  cardinality of a minimum monophonic eccentric  dominating set of G. We investigate some properties of monophonic eccentric  dominating sets. Also, we determine the bounds of monophonic eccentric  domination number and find the same for some standard graphs.

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References

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Communications in Combinatorics and Optimization
Volume 9, Issue 4
December 2024
Pages 625-633

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