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On regular graphs equienergetic with their complements
Abstract
Iboostup premium 6 8 28 cm. We give necessary and sufficient conditions on the parameters of a regular graph $Gamma$ such that $E(Gamma)=E(bar Gamma)$. Then we show that, up to complements, the only bipartite regular graphs equienergetic and non-isospectral with their complements are the crown graphs or $C_4$. Next, for the family of strongly regular graphs $Gamma$ we characterize all possible parameters $srg(n,k,e,d)$ such that $E(Gamma) = E(bar Gamma)$. Furthermore, using this, we prove that a strongly regular graph is equienergetic to its complement if and only if it is either a conference graph or else it is a pseudo Latin square graph (i.e.@ has $OA$ parameters). Ip scanner pro 3 94 32. We also characterize all complementary equienergetic pairs of graphs of type $C(2)$, $C(3)$ and $C(5)$ in Cameron's hierarchy. Finally, we consider unitary Cayley graphs over rings $G_R=X(R,R^*)$. We showed that if $R$ is a finite artinian ring with an even number of local factors, then $G_R$ is equienergetic with its complement if and only if $R=mathbb{F}_{q} times mathbb{F}_{q'}$ is the product of 2 finite fields. Starcraft ii 4 3 2.
Ipack 2 3 4 X 5 6
Ipack 2 3 4 X 5 6 As A Fraction
Ipack 2 3 4 X 5 6 Fraction
- Mathematics - Combinatorics
Ipack 2 3 4 X 5
