IMI/Publicaţii/CSJM/Ediţii/CSJM v.25, n.3 (75), 2017/

On the locating matrix of a graph and its spectral analysis

Authors: H. N. Ramaswamy, Anwar Alwardi, N. Ravi Kumar
Keywords: Locating eigenvalues (of graph), Locating Spect\-rum (of graph), Locating energy (of graph).


We introduce a new matrix representation for a graph by defining the locating matrix $\mathbf{Lo}(G)$ of $G$. We define the locating eigenvalues, the locating spectrum, and locating energy of the graph and we calculate them for some standard graphs. We also obtain bounds for the locating energy for regular and strongly regular graphs.

H. N. Ramaswamy
Department of Studies in Mathematics
University of Mysore, Manasagangothri,
Mysore - 570 006, INDIA

Anwar Alwardi
Department of Mathematics,
College of Education, Yafea,
University of Aden
Yemen, Aden

N. Ravi Kumar
Department of Mathematics,
Government First Grade College,
Gundulpet - 571111, India.


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