ON MONOPHONIC ECCENTRIC SEQUENCES OF GRAPHS

ON MONOPHONIC ECCENTRIC SEQUENCES OF GRAPHS

Diya Jaji, Tabitha Agnes Mangam, H. R. Deepika

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Abstract

For a connected graph G and a vertex v ∈ V (G), the eccentricity e(v) is the maximum distance from v to any other vertex in G. A path P in G is called a monophonic path if it is chordless. The monophonic distance dm(u, v) between two vertices u and v is the length of a longest chordless u–v path in G. The monophonic eccentricity of a vertex v, denoted by em(v), is defined as the maximum monophonic distance between v and any other vertex of G. In this paper, we investigate monophonic eccentric sequences for several classes of graphs. In particular, we determine these sequences for unicyclic graphs and the Petersen graph, and obtain characterizations related to monophonic eccentricities in these graph classes.

Keywords

diameter, eccentricity, eccentric sequence, monophonic distance, monophonic eccentric sequence.