Computing Metric Dimension of Certain Families of Toeplitz Graphs

IEEE Access

Muhammad Faisal Nadeem¹  Wajiha Nazir¹  Hafiz Muhammad Afzal Siddiqui¹  Jia-Bao Liu² 

[1] Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan;School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China;

关键词: Metric dimension;    basis;    resolving set;    Toeplitz graph;   

DOI  :  10.1109/ACCESS.2019.2938579

来源: DOAJ

【 摘 要 】

The position of a moving point in a connected graph can be identified by computing the distance from the point to a set of sonar stations which have been appropriately situated in the graph. Let Q = {q₁, q₂, ... , q_k} be an ordered set of vertices of a graph G and a is any vertex in G, then the code/representation of a w.r.t Q is the k-tuple (r(a, q₁), r(a, q₂), ... , r(a, q_k)), denoted by r(a|Q). If the different vertices of G have the different representations w.r.t Q, then Q is known as a resolving set/locating set. A resolving/locating set having the least number of vertices is the basis for G and the number of vertices in the basis is called metric dimension of G and it is represented as dim(G). In this paper, the metric dimension of Toeplitz graphs generated by two and three parameters denoted by T_n〈1, t〉 and T_n〈1, 2, t〉, respectively is discussed and proved that it is constant.

【 授权许可】

Unknown