IJPAM: Volume 89, No. 4 (2013)

LAPLACIAN MINIMUM DOMINATING ENERGY
OF A GRAPH

M.R. Rajesh Kanna$^1$, B.N. Dharmendra$^2$, G. Sridhara$^3$
$^{1,2,3}$Post Graduate Department of Mathematics
Maharani's Science College for Women
J.L.B. Road, Mysore, 570 005, INDIA
$^3$Research Scholar
Research and Development Centre
Bharathiar University
Coimbatore, 641 046, INDIA


Abstract. Recently Prof.Chandrashekara adiga et al. [1] defined the minimum covering energy, $E_C(G)$ of a graph which depends on its particular minimum cover $C$. Motivated by this, we introduced minimum dominating energy [17] of a graph $E_D(G)$. In this paper we computed Laplacian minimum dominating energies of star graph, complete graph, crown graph and cocktail party graphs. Upper and lower bounds for $LE_D(G)$ are established.

Received: August 30, 2013

AMS Subject Classification: 05C50, 05C69

Key Words and Phrases: minimum dominating set, Laplacian minimum dominating matrix, Laplacian minimum dominating eigenvalues, Laplacian minimum dominating energy of a graph

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DOI: 10.12732/ijpam.v89i4.11 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 4