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Abstract
In this correspondence, we introduced the concept of minimum roman dominating distance energy ERDd(G) of a graph G and computed minimum roman dominating distance energy of some standard graphs. Also, we discussed the properties of eigenvalues of a minimum roman dominating distance matrix ARDd(G). Finally, we derived the upper and lower bounds for ERDd(G).
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References
- Bapat, R. B., Graphs and Matrices, Hindustan Book Agency, 2011.
- Bapat, R., Kirkland, S. J. and Neumann, M., On distance matrices and Laplacians, Linear Algebra and its Applications, 401 (2005), 193-209.
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- Rajesh Kanna, M.R., Dharmendra, B. N. and Pradeep Kumar, R., Minimum covering distance energy of a graph, Applied Mathematical Sciences, 7(111) (2013), 5525-5536.
- Rajesh Kanna, M.R., Dharmendra, B. N. and Sridhara, G., Minimum dominating distance
- energy of a graph, Journal of Indonesian Mathematical Society, 20(1) (2014), 19-29.
- Rajesh Kanna, M. R., Dharmendra, B. N. and Sridhara, G., Laplacian minimum dominating
- energy of a graph, International Journal of Pure and Applied Mathematics, 89(4) (2013), 565-581
References
Bapat, R. B., Graphs and Matrices, Hindustan Book Agency, 2011.
Bapat, R., Kirkland, S. J. and Neumann, M., On distance matrices and Laplacians, Linear Algebra and its Applications, 401 (2005), 193-209.
Cockayne, E.J., Paul A Dreyer Jr., Sandra M Hedetniemi and Hedetniemi, S.T., Roman domination in graphs, Discrete Mathematics, 278 (2004), 11-22.
Graham, R. L., Hoffman, A. J. and Hosoya, H., On the distance matrix of a directed graph, Journal of Graph Theory, 1(1) (1977), 85-88.
Graham, R. L. and Lov´asz, L., Distance matrix polynomials of trees, Advances in Mathematics, 29(1) (1978), 60-88.
Graham, R. L. and Pollak, H. O., On the addressing problem for loop switching, The Bell
System Technical Journal, 50 (1971), 2495-2519.
Gutman, I., The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz. Graz, 103 (1978), 1-22.
Rajesh Kanna, M.R., Dharmendra, B. N. and Pradeep Kumar, R., Minimum covering distance energy of a graph, Applied Mathematical Sciences, 7(111) (2013), 5525-5536.
Rajesh Kanna, M.R., Dharmendra, B. N. and Sridhara, G., Minimum dominating distance
energy of a graph, Journal of Indonesian Mathematical Society, 20(1) (2014), 19-29.
Rajesh Kanna, M. R., Dharmendra, B. N. and Sridhara, G., Laplacian minimum dominating
energy of a graph, International Journal of Pure and Applied Mathematics, 89(4) (2013), 565-581