Signed bicyclic graphs with minimal index

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Brunetti Maurizio; Ciampella Adriana

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Journal Paper

Paper Information

Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2023 | Volume:8 | Issue:1 Page(s): 207-241

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Information Journal Paper

Title

Signed bicyclic graphs with minimal index

Author(s)

Brunetti Maurizio | Ciampella Adriana | Issue Writer Certificate

Keywords

Signed Graph

Bicyclic Graph

Index

Extremal Graph Theory

Abstract

The Index λ, 1(ґ, ) of a Signed Graph ґ,= (G,σ, ) is just the largest eigenvalue of its adjacency matrix. For any n > 4 we identify the Signed Graphs achieving the minimum Index in the class of signed Bicyclic Graphs with n vertices. Apart from the n = 4 case, such graphs are obtained by considering a starlike tree with four branches of suitable length (i. e. four distinct paths joined at their end vertex u) with two additional negative independent edges pairwise joining the four vertices adjacent to u. As a by-product, all signed Bicyclic Graphs containing a theta-graph and whose Index is less than 2 are detected.

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APA: Copy

Brunetti, Maurizio, & Ciampella, Adriana. (2023). Signed bicyclic graphs with minimal index. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 8(1), 207-241. SID. https://sid.ir/paper/1057950/en

Vancouver: Copy

Brunetti Maurizio, Ciampella Adriana. Signed bicyclic graphs with minimal index. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION[Internet]. 2023;8(1):207-241. Available from: https://sid.ir/paper/1057950/en

IEEE: Copy

Maurizio Brunetti, and Adriana Ciampella, “Signed bicyclic graphs with minimal index,” COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, vol. 8, no. 1, pp. 207–241, 2023, [Online]. Available: https://sid.ir/paper/1057950/en

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