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)