Extreme outer connected monophonic graphs

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Ganesamoorthy K.; Lakshmi Priya S.

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Journal Paper

Paper Information

Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2022 | Volume:7 | Issue:2 Page(s): 211-226

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Information Journal Paper

Title

Extreme outer connected monophonic graphs

Author(s)

Ganesamoorthy K. | Lakshmi Priya S. | Issue Writer Certificate

Keywords

outer connected monophonic set

outer connected monophonic number

extreme order

extreme outer connected monophonic graph

Abstract

For a connected graph G of order at least two, a set S of vertices in a graph G is said to be an outer connected monophonic set if S is a monophonic set of G and either S = V or the subgraph induced by V-S is connected. The minimum cardinality of an outer connected monophonic set of G is the outer connected monophonic number of G and is denoted by moc (G). The number of extreme vertices in G is its extreme order ex(G). A graph G is said to be an extreme outer connected monophonic graph if moc(G) = ex(G). extreme outer connected monophonic graphs of order p with outer connected monophonic number p and extreme outer connected monophonic graphs of order p with outer connected monophonic number p-1 are characterized. It is shown that for every pair a,b of integers with 0 ≥,a ≥,b and b ≥,2, there exists a connected graph G with ex(G) = a and moc(G) = b. Also, it is shown that for positive integers r,d and k≥, 2 with r < d, there exists an extreme outer connected monophonic graph G with monophonic radius r, monophonic diameter d and outer connected monophonic number k.

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APA: Copy

Ganesamoorthy, K., & Lakshmi Priya, S.. (2022). Extreme outer connected monophonic graphs. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 7(2), 211-226. SID. https://sid.ir/paper/1057908/en

Vancouver: Copy

Ganesamoorthy K., Lakshmi Priya S.. Extreme outer connected monophonic graphs. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION[Internet]. 2022;7(2):211-226. Available from: https://sid.ir/paper/1057908/en

IEEE: Copy

K. Ganesamoorthy, and S. Lakshmi Priya, “Extreme outer connected monophonic graphs,” COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, vol. 7, no. 2, pp. 211–226, 2022, [Online]. Available: https://sid.ir/paper/1057908/en

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