Opuscula Math. 38, no. 1 (2018), 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

B. R. Rakshith

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.

Full text (pdf)

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• University of Mysore, Manasagangothri, Department of Studies in Mathematics, Mysuru - 570 006, India
• B. R. Rakshith
• University of Mysore, Manasagangothri, Department of Studies in Mathematics, Mysuru - 570 006, India
• Communicated by Adam Paweł Wojda.
• Accepted: 2017-06-14.
• Published online: 2017-11-13.