Bicyclic signed graphs with minimal and second minimal energy

Bhat, Mushtaq A.; Samee, U.; Pirzada, S.

doi:10.1016/j.laa.2018.03.047

Cited by 9 publications

(12 citation statements)

References 21 publications

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“…Lemma 5 (see [14]). Among all bicyclic signed graphs with n ≥ 8 vertices, S 1 n,n+1 and S 3 n,n+1 have the minimal energy.…”

Section: Lemma 3 (See [2]) E(s N ) ≤ E(t N ) ≤ E(p N ) With Equalitmentioning

confidence: 99%

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Research on Extreme Signed Graphs with Minimal Energy in Tricyclic Signed Graphs S(n, n + 2)

Wang

Gao

2020

Complexity

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“…Lemma 5 (see [14]). Among all bicyclic signed graphs with n ≥ 8 vertices, S 1 n,n+1 and S 3 n,n+1 have the minimal energy.…”

Section: Lemma 3 (See [2]) E(s N ) ≤ E(t N ) ≤ E(p N ) With Equalitmentioning

confidence: 99%

“…e conjecture is true for unicyclic, bicyclic, and tricyclic graphs [9][10][11][12]. A signed analogue of this conjecture is true when m � n for n ≥ 6 in [13] and when m � n + 1 for n ≥ 12 in [14]. In this paper, we consider the above conjecture for signed graphs, in the case m � n + 2 for n ≥ 14.…”

Section: Introductionmentioning

confidence: 99%

Research on Extreme Signed Graphs with Minimal Energy in Tricyclic Signed Graphs S(n, n + 2)

Wang

Gao

2020

Complexity

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“…Bhat and Pirzada [2] characterized the unicyclic signed graphs with minimal energy. Bhat et al [4], characterized the bicyclic signed graphs with minimal and second minimal energy. Similar problems for graphs, digraphs, signed graphs and signed digraphs have been studied in [3,5,9,10,11,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

“…Switching equivalence is an equivalence relation on the signings of a fixed graph. For more details about switching see [4,15]. An equivalence class is called a switching class.…”

Section: Introductionmentioning

confidence: 99%

On ordering of minimal energies in bicyclic signed graphs

Pirzada

Shamsher

Bhat

2021

Acta Universitatis Sapientiae, Informatica

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Let S = (G, σ) be a signed graph of order n and size m and let x1, x2, ..., xn be the eigenvalues of S. The energy of S is defined as ɛ ( S ) = ∑ j = 1 n | x j | \varepsilon \left( S \right) = \sum\limits_{j = 1}^n {\left| {{x_j}} \right|} . A connected signed graph is said to be bicyclic if m=n + 1. In this paper, we determine the bicyclic signed graphs with first 20 minimal energies for all n ≥ 30 and with first 16 minimal energies for all 17 ≤ n ≤ 29.

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“…Among all the unicyclic signed graphs with n vertices, Bhat and Pirzada [4] characterized the unicyclic signed graph with the minimal energy. Among all the bicyclic signed graphs with n vertices, Bhat et al [5] determined the bicyclic signed graphs with the first and the second minimal energies.…”

Section: Introductionmentioning

confidence: 99%

Ordering of the unicyclic signed graphs with perfect matchings by their minimal energies

Liu

Wang

2020

Filomat

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Let U?2n be the set of unicyclic signed graphs with perfect matchings having 2n vertices, where ? is a signing function from the edge set of the graphs considered to {-1,1}. The increasing order of the signed graphs among U?2n according to their minimal energies is considered. A relationship between the energies of a unicyclic graph and of its signed graphs is derived. A new integral formula for comparing the energies of two signed graph is introduced. In U?2n with n ? 721, the first 18 signed graphs in the increasing order by their minimal energies are obtained.

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Bicyclic signed graphs with minimal and second minimal energy

Cited by 9 publications

References 21 publications

Research on Extreme Signed Graphs with Minimal Energy in Tricyclic Signed Graphs S(n, n + 2)

Research on Extreme Signed Graphs with Minimal Energy in Tricyclic Signed Graphs S(n, n + 2)

On ordering of minimal energies in bicyclic signed graphs

Ordering of the unicyclic signed graphs with perfect matchings by their minimal energies

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