Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287777358> ?p ?o ?g. }
Showing items 1 to 55 of
55
with 100 items per page.
- W4287777358 abstract "A $mathbb{T}$-gain graph, $Phi = (G, varphi)$, is a graph in which the function $varphi$ assigns a unit complex number to each orientation of an edge, and its inverse is assigned to the opposite orientation. The associated adjacency matrix $ A(Phi) $ is defined canonically. The energy $ mathcal{E}(Phi) $ of a $ mathbb{T} $-gain graph $ Phi $ is the sum of the absolute values of all eigenvalues of $ A(Phi) $. We study the notion of energy of a vertex of a $ mathbb{T} $-gain graph, and establish bounds for it. For any $ mathbb{T} $-gain graph $ Phi$, we prove that $2tau(G)-2c(G) leq mathcal{E}(Phi) leq 2tau(G)sqrt{Delta(G)}$, where $ tau(G), c(G)$ and $ Delta(G)$ are the vertex cover number, the number of odd cycles and the largest vertex degree of $ G $, respectively. Furthermore, using the properties of vertex energy, we characterize the classes of $ mathbb{T} $-gain graphs for which $ mathcal{E}(Phi)=2tau(G)-2c(G) $ holds. Also, we characterize the classes of $ mathbb{T} $-gain graphs for which $mathcal{E}(Phi)= 2tau(G)sqrt{Delta(G)} $ holds. This characterization solves a general version of an open problem. In addition, we establish bounds for the energy in terms of the spectral radius of the associated adjacency matrix." @default.
- W4287777358 created "2022-07-26" @default.
- W4287777358 creator A5004182819 @default.
- W4287777358 creator A5055254203 @default.
- W4287777358 date "2020-05-18" @default.
- W4287777358 modified "2023-09-29" @default.
- W4287777358 title "Bounds for the energy of a complex unit gain graph" @default.
- W4287777358 doi "https://doi.org/10.48550/arxiv.2005.08634" @default.
- W4287777358 hasPublicationYear "2020" @default.
- W4287777358 type Work @default.
- W4287777358 citedByCount "0" @default.
- W4287777358 crossrefType "posted-content" @default.
- W4287777358 hasAuthorship W4287777358A5004182819 @default.
- W4287777358 hasAuthorship W4287777358A5055254203 @default.
- W4287777358 hasBestOaLocation W42877773581 @default.
- W4287777358 hasConcept C114614502 @default.
- W4287777358 hasConcept C118615104 @default.
- W4287777358 hasConcept C121332964 @default.
- W4287777358 hasConcept C132525143 @default.
- W4287777358 hasConcept C140532419 @default.
- W4287777358 hasConcept C158693339 @default.
- W4287777358 hasConcept C180356752 @default.
- W4287777358 hasConcept C207467116 @default.
- W4287777358 hasConcept C2524010 @default.
- W4287777358 hasConcept C33923547 @default.
- W4287777358 hasConcept C62520636 @default.
- W4287777358 hasConcept C80899671 @default.
- W4287777358 hasConceptScore W4287777358C114614502 @default.
- W4287777358 hasConceptScore W4287777358C118615104 @default.
- W4287777358 hasConceptScore W4287777358C121332964 @default.
- W4287777358 hasConceptScore W4287777358C132525143 @default.
- W4287777358 hasConceptScore W4287777358C140532419 @default.
- W4287777358 hasConceptScore W4287777358C158693339 @default.
- W4287777358 hasConceptScore W4287777358C180356752 @default.
- W4287777358 hasConceptScore W4287777358C207467116 @default.
- W4287777358 hasConceptScore W4287777358C2524010 @default.
- W4287777358 hasConceptScore W4287777358C33923547 @default.
- W4287777358 hasConceptScore W4287777358C62520636 @default.
- W4287777358 hasConceptScore W4287777358C80899671 @default.
- W4287777358 hasLocation W42877773581 @default.
- W4287777358 hasOpenAccess W4287777358 @default.
- W4287777358 hasPrimaryLocation W42877773581 @default.
- W4287777358 hasRelatedWork W11236532 @default.
- W4287777358 hasRelatedWork W14658856 @default.
- W4287777358 hasRelatedWork W1563924 @default.
- W4287777358 hasRelatedWork W18687971 @default.
- W4287777358 hasRelatedWork W24921706 @default.
- W4287777358 hasRelatedWork W25624111 @default.
- W4287777358 hasRelatedWork W25648989 @default.
- W4287777358 hasRelatedWork W28586905 @default.
- W4287777358 hasRelatedWork W9333331 @default.
- W4287777358 hasRelatedWork W13577648 @default.
- W4287777358 isParatext "false" @default.
- W4287777358 isRetracted "false" @default.
- W4287777358 workType "article" @default.