A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION

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Mohagheghi Nezhad Mostafa; Rahbarnia Freydoon; Mirzavaziri Madjid; GHANBARI REZA

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Journal: JOURNAL OF ALGEBRAIC SYSTEMS Year:2020 | Volume:7 | Issue:2 Page(s): 179-187

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Information Journal Paper

Title

A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION

Author(s)

Mohagheghi Nezhad Mostafa | Rahbarnia Freydoon | Mirzavaziri Madjid | GHANBARI REZA | Issue Writer Certificate

Keywords

Metric dimension

Resolving set

Metric basis

Basic distance

Contour of a graph

Abstract

The \textit{Metric dimension} of a connected graph GG is the minimum number of vertices in a subset BB of GG such that all other vertices are uniquely determined by their distances to the vertices in BB. In this case, BB is called a \textit{Metric basis} for GG. The \textit{Basic distance} of a metric two dimensional graph GG is the distance between the elements of BB. Giving a characterization for those graphs whose Metric dimensions are two, we enumerate the number of nn vertex metric two dimensional graphs with Basic distance 1.

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APA: Copy

Mohagheghi Nezhad, Mostafa, Rahbarnia, Freydoon, Mirzavaziri, Madjid, & GHANBARI, REZA. (2020). A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION. JOURNAL OF ALGEBRAIC SYSTEMS, 7(2 ), 179-187. SID. https://sid.ir/paper/268366/en

Vancouver: Copy

Mohagheghi Nezhad Mostafa, Rahbarnia Freydoon, Mirzavaziri Madjid, GHANBARI REZA. A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2020;7(2 ):179-187. Available from: https://sid.ir/paper/268366/en

IEEE: Copy

Mostafa Mohagheghi Nezhad, Freydoon Rahbarnia, Madjid Mirzavaziri, and REZA GHANBARI, “A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 7, no. 2 , pp. 179–187, 2020, [Online]. Available: https://sid.ir/paper/268366/en

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