ON THE MONOPHONIC AND MONOPHONIC DOMINATION POLYNOMIAL OF A GRAPH

A set S of vertices of a graph G is a monophonic set of G if each vertex u of G lies on an u--v monophonic path in G for some u,v [member of] S. M [??] V(G) is said to be a monophonic dominating set if it is both a monophonic set and a dominating set. Let M(G, i) be the family of monophonic sets of...

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Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics 2024-01, Vol.14 (1), p.197
Main Authors: Sudhahar, P.A.P, Jebi, W
Format: Article
Language:English
Subjects:
Apexes
Fuzzy sets
Graph theory
Graphs
Mathematical research
Mathematics
Polynomials
Set theory
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Summary:A set S of vertices of a graph G is a monophonic set of G if each vertex u of G lies on an u--v monophonic path in G for some u,v [member of] S. M [??] V(G) is said to be a monophonic dominating set if it is both a monophonic set and a dominating set. Let M(G, i) be the family of monophonic sets of a graph G with cardinality i and let m(G,i) = |M(G,i)|. Then the monophonic polynomial M(G, x) of G is defined as M(G, x) = [??] (G, i)[x.sup.i], where m(G) is the monophonic number of G. In this article, we have introduced monophonic domination polynomial of a graph. We have computed the monophonic and monophonic domination polynomials of some specific graphs. In addition, monophonic and monophonic domination polynomial of the corona product of two graphs is derived. Keywords: Monophonic set, Monophonic Dominating set, Monophonic polynomial, Monophonic domination polynomial, Corona product. AMS Subject Classification: 05C12, 05C69.
ISSN:2146-1147
2146-1147