Clique-to-vertex monophonic distance in graphs
| Autor: | I Keerthi Asir, S Athisayanathan |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Vertex (graph theory)
Geodesic Computer Science::Information Retrieval 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 0102 computer and information sciences 01 natural sciences Combinatorics Computer Science::Discrete Mathematics 010201 computation theory & mathematics Computer Science::General Literature Discrete Mathematics and Combinatorics 0101 mathematics Connectivity Mathematics |
| Zdroj: | Discrete Mathematics, Algorithms and Applications. :1750004 |
| ISSN: | 1793-8317 1793-8309 |
| DOI: | 10.1142/s1793830917500045 |
| Popis: | In this paper, we define the clique-to-vertex [Formula: see text]–[Formula: see text] monophonic path, the clique-to-vertex monophonic distance [Formula: see text], the clique-to-vertex monophonic eccentricity [Formula: see text], the clique-to-vertex monophonic radius [Formula: see text], and the clique-to-vertex monophonic diameter [Formula: see text], where [Formula: see text] is a clique and [Formula: see text] a vertex in a connected graph [Formula: see text]. We determine these parameters for some standard graphs. We show the inequality among the clique-to-vertex distance, the clique-to-vertex monophonic distance, and the clique-to-vertex detour distance in graphs. Also, it is shown that the clique-to-vertex geodesic, the clique-to-vertex monophonic, and the clique-to-vertex detour are distinct in [Formula: see text]. It is shown that [Formula: see text] for every connected graph [Formula: see text] and that every two positive integers [Formula: see text] and [Formula: see text] with [Formula: see text] are realizable as the clique-to-vertex monophonic radius and clique-to-vertex monophonic diameter of some connected graph. Also, it is shown any three positive integers [Formula: see text] with [Formula: see text] are realizable as the clique-to-vertex radius, clique-to-vertex monophonic radius, and clique-to-vertex detour radius of some connected graph and also it is shown that any three positive integers [Formula: see text] with [Formula: see text] are realizable as the clique-to-vertex diameter, clique-to-vertex monophonic diameter, and clique-to-vertex detour diameter of some connected graph. We introduce the clique-to-vertex monophonic center [Formula: see text] and the clique-to-vertex monophonic periphery [Formula: see text] and it is shown that the clique-to-vertex monophonic center does not lie in a single block of [Formula: see text]. |
| Databáze: | OpenAIRE |
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