Research ArticleNo Access

Characterizations of graphs with prescribed connected detour numbers

Ahmed M. Ali

https://orcid.org/0000-0002-3794-2785

Department of Mathematics/College of Computers Sciences and Mathematics, University of Mosul, Iraq

E-mail Address: ahmedgraph@uomosul.edu.iq

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and

Ali A. Ali

Department of Mathematics/College of Computers Sciences and Mathematics, University of Mosul, Iraq

E-mail Address: aliazizali1933@yahoo.com

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https://doi.org/10.1142/S1793557121501345Cited by:0 (Source: Crossref)

Abstract

Let $G$ be a $(p$ , $q)$ - graph, $D (G)$ the detour diameter of $G$ , and cdn $(G)$ is the connected detour number of $G$ . Santhakumaran and Athisayanathan are characterized by the graphs of $D (G) \leq$ 4 and cdn $(G) = p$ , $p - 1$ and $p - 2$ . In this paper, we obtain a necessary and sufficient condition for a graph $G$ , $p (G) \geq$ 2, of $D (G) \leq$ 8 to have cdn $(G) = p$ . Moreover, graphs G of $p (G) \geq$ 6, and $D (G)$ = 5 and 6, such that cdn $(G) = p - 1$ , are characterized in this research.

Communicated by H. Tanaka

Keywords:

AMSC: 26D07, 26B35

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