The authors prove that for a unicyclic graph G on n vertices with odd cycle length k, s+(G) > n > s-(G) when k ≡ 3 mod 4 and s+(G) < n < s-(G) when k ≡ 1 mod 4.
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A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs
The authors prove that for a unicyclic graph G on n vertices with odd cycle length k, s+(G) > n > s-(G) when k ≡ 3 mod 4 and s+(G) < n < s-(G) when k ≡ 1 mod 4.