Opuscula Mathematica
Opuscula Math. 38, no. 1 (), 5-13
https://doi.org/10.7494/OpMath.2018.38.1.5
Opuscula Mathematica

Upper bounds for the extended energy of graphs and some extended equienergetic graphs



Abstract. In this paper, we give two upper bounds for the extended energy of a graph one in terms of ordinary energy, maximum degree and minimum degree of a graph, and another bound in terms of forgotten index, inverse degree sum, order of a graph and minimum degree of a graph which improves an upper bound of Das et al. from [On spectral radius and energy of extended adjacency matrix of graphs, Appl. Math. Comput. 296 (2017), 116-123]. We present a pair of extended equienergetic graphs on \(n\) vertices for \(n\equiv 0(\text{mod } 8)\) starting with a pair of extended equienergetic non regular graphs on \(8\) vertices and also we construct a pair of extended equienergetic graphs on \(n\) vertices for all \(n\geq 9\) starting with a pair of equienergetic regular graphs on \(9\) vertices.
Keywords: energy of a graph, extended energy of a graph, extended equienergetic graphs.
Mathematics Subject Classification: 05C50.
Cite this article as:
Chandrashekar Adiga, B. R. Rakshith, Upper bounds for the extended energy of graphs and some extended equienergetic graphs, Opuscula Math. 38, no. 1 (2018), 5-13, https://doi.org/10.7494/OpMath.2018.38.1.5
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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