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Relevant bibliographies by topics / Vertex monophonic number

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Journal articles

Academic literature on the topic 'Vertex monophonic number'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Vertex monophonic number"

1

Santhakumaran, A. P., P. Titus, and K. Ganesamoorthy. "Edge-to-vertex m-detour monophonic number of a graph." Proyecciones (Antofagasta) 37, no. 3 (2018): 415–28. https://doi.org/10.22199/issn.0717-6279-3161.

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For a connected graph G = (V, E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. A u − v path of length dm(u, v) is called a u − v detour monophonic. For subsets A and B of V, the m-monophonic distance Dm(A, B) is defined as Dm(A, B) = max{dm(x, y) : x ∈ A, y ∈ B}. A u − v path of length Dm(A, B) is called a A − B m-detour monophonic path joining the sets A, B ⊆ V, where u ∈ A and v ∈ B. A set S ⊆ E is called an edge-to-vertex m-detour monophonic set of G if every vertex of G is incident with an edge of S or lies on a m-detour mo

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2

Titus, P., M. Subha, and S. Santha Kumari. "Monophonic graphoidal covering number of corona product graphs." Proyecciones (Antofagasta) 42, no. 2 (2023): 303–18. http://dx.doi.org/10.22199/issn.0717-6279-4781.

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In a graph G, a chordless path is called a monophonic path. A collection ψm of monophonic paths in G is called a monophonic graphoidal cover of G if every vertex of G is an internal vertex of at most one monophonic path in ψm and every edge of G is in exactly one monophonic path in ψm. The monophonic graphoidal covering number ηm(G) of G is the minimum cardinality of a monophonic graphoidal cover of G. In this paper, we find the monophonic graphoidal covering number of corona product of some standard graphs.

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3

JOHN, J., and K. UMA SAMUNDESVARI. "THE FORCING EDGE FIXING EDGE-TO-VERTEX MONOPHONIC NUMBER OF A GRAPH." Discrete Mathematics, Algorithms and Applications 05, no. 04 (2013): 1350034. http://dx.doi.org/10.1142/s1793830913500341.

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For a connected graph G = (V, E), a set Se ⊆ E(G)–{e} is called an edge fixing edge-to-vertex monophonic set of an edge e of a connected graph G if every vertex of G lies on an e – f edge-to-vertex monophonic path of G, where f ∈ Se. The edge fixing edge-to-vertex monophonic number mefev(G) of G is the minimum cardinality of its edge fixing edge-to-vertex monophonic sets of an edge e of G. A subset Me ⊆ Se in a connected graph G is called a forcing subset for Se, if Se is the unique edge fixing edge-to-vertex monophonic set of e of G containing Me. A forcing subset for Se of minimum cardinalit

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4

Gamorez, Anabel, and Sergio Canoy Jr. "Monophonic Eccentric Domination Numbers of Graphs." European Journal of Pure and Applied Mathematics 15, no. 2 (2022): 635–45. http://dx.doi.org/10.29020/nybg.ejpam.v15i2.4354.

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Let G be a (simple) undirected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is a monophonic eccentric dominating set if every vertex in V (G) \ S has a monophonic eccentric vertex in S. The minimum size of a monophonic eccentric dominating set in G is called the monophonic eccentric domination number of G. It is shown that the absolute difference of the domination number and monophonic eccentric domination number of a graph can be made arbitrarily large. We characterize the monophonic eccentric dominating sets in graphs resulting from the join, corona, and lexi

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5

John, J., P. Arul Paul Sudhahar, and D. Stalin. "On the (M,D) number of a graph." Proyecciones (Antofagasta) 38, no. 2 (2019): 255–66. https://doi.org/10.22199/issn.0717-6279-3570.

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For a connected graph G = (V, E), a monophonic set of G is a set M ⊆ V (G) such that every vertex of G is contained in a monophonic path joining some pair of vertices in M. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbour in D. A monophonic dominating set M is both a monophonic and a dominating set. The monophonic, dominating, monophonic domination number m(G), γ(G), γm(G) respectively are the minimum cardinality of the respective sets in G. Monophonic domination number of certain classes of graphs are determined. Connected graph of order

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6

Lourdusamy, A., S. Kither Iammal, and I. Dhivviyanandam. "Monophonic Cover Pebbling Number \((MCPN)\) of Network Graphs." Utilitas Mathematica 121, no. 1 (2024): 11–24. https://doi.org/10.61091/um121-02.

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Given a connected graph \(G\) and a configuration \(D\) of pebbles on the vertices of \(G\), a pebbling transformation involves removing two pebbles from one vertex and placing one pebble on its adjacent vertex. A monophonic path is defined as a chordless path between two non-adjacent vertices \(u\) and \(v\). The monophonic cover pebbling number, \(\gamma_{\mu}(G)\), is the minimum number of pebbles required to ensure that, after a series of pebbling transformations using monophonic paths, all vertices of \(G\) are covered with at least one pebble each. In this paper, we determine the monopho

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7

K., Ponselvi. "THE MONOPHONIC DIAMETRAL PATH FIXING MONOPHONIC NUMBER OF A GRAPH." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 5 (2018): 66–69. https://doi.org/10.5281/zenodo.1251655.

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For a connected graph , let  be amonophonic diametral path of . A set  is called a monophonic set of  if every vertex of  lies on a  monophonic pathwhere and . The minimum cardinality of a  monophonic set of  is monophonic number of denoted by . A monophonic set of cardinality  is called a set of<em>G</em>. monophonic number of  certain classes of graphs are studied. Connected graphs of order  with monophonic number  and  are characterized. It is shown that for integers with , there exists a connected graph  of order , with and .

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8

Titus, P., and S. Eldin Vanaja. "Edge fixed monophonic number of a graph." Proyecciones (Antofagasta) 36, no. 3 (2017): 363–72. https://doi.org/10.22199/issn.0717-6279-2381.

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For an edge xy in a connected graph G of order p ≥ 3, a set SCV(G)is an xy-monophonic set of G if each vertex v Є V(G) lies on an x-u monophonic path or a y-u monophonic path for some element u in S. The minimum cardinality of an xy- monophonic set of G is defined as the xy-monophonic number of G, denoted by mxy (G). An xy-monophonic set of cardinality mxy (G) is called a mxy -set of G. We determine bounds for it and find the same for special classes of graphs. It is shown that for any three positive integers r, d and n ≥ 2 with 2 ≤ r ≤ d, there exists a connected graph G with monophonic radiu

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9

Santhakumaran, A. P., and P. Titus. "The vertex monophonic number of a graph." Discussiones Mathematicae Graph Theory 32, no. 2 (2012): 191. http://dx.doi.org/10.7151/dmgt.1599.

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10

Santhakumaran, A. P., and T. Venkata Raghu. "Upper double monophonic number of a graph." Proyecciones (Antofagasta) 37, no. 2 (2018): 295–304. https://doi.org/10.22199/issn.0717-6279-2929.

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A set S of a connected graph G of order n is called a double monophonic set of G if for every pair of vertices x, y in G there exist vertices u, v in S such that x, y lie on a u - v monophonic path. The double monophonic number dm(G) of G is the minimum cardinality of a double monophonic set. A double monophonic set S in a connected graph G is called a minimal double monophonic set if no proper subset of S is a double monophonic set of G. The upper double monophonic number of G is the maximum cardinality of a minimal double monophonic set of G, and is denoted by dm+(G). Some general properties

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