Matches in SemOpenAlex for { <https://semopenalex.org/work/W4280510305> ?p ?o ?g. }
Showing items 1 to 45 of
45
with 100 items per page.
- W4280510305 abstract "Let $G$ be a triangle-free graph on $n$ vertices with adjacency matrix eigenvalues $mu_1(G)geq mu_2(G)geq dots geq mu_n(G)$. In this paper we study the quantity $$mu_1(G)+mu_n(G).$$ We prove that for any triangle-free graph $G$ we have $$mu_1(G)+mu_n(G)leq (3-2sqrt{2})n.$$ This was proved for regular graphs by Brandt, we show that the condition on regularity is not necessary. We also prove that among triangle-free strongly regular graphs the Higman-Sims graph achieves the maximum of $$frac{mu_1(G)+mu_n(G)}{n}.$$" @default.
- W4280510305 created "2022-05-22" @default.
- W4280510305 creator A5073644023 @default.
- W4280510305 date "2022-05-18" @default.
- W4280510305 modified "2023-10-14" @default.
- W4280510305 title "Note on the sum of the smallest and largest eigenvalues of a triangle-free graph" @default.
- W4280510305 doi "https://doi.org/10.48550/arxiv.2205.08873" @default.
- W4280510305 hasPublicationYear "2022" @default.
- W4280510305 type Work @default.
- W4280510305 citedByCount "0" @default.
- W4280510305 crossrefType "posted-content" @default.
- W4280510305 hasAuthorship W4280510305A5073644023 @default.
- W4280510305 hasBestOaLocation W42805103051 @default.
- W4280510305 hasConcept C114614502 @default.
- W4280510305 hasConcept C118615104 @default.
- W4280510305 hasConcept C121332964 @default.
- W4280510305 hasConcept C132525143 @default.
- W4280510305 hasConcept C158693339 @default.
- W4280510305 hasConcept C180356752 @default.
- W4280510305 hasConcept C33923547 @default.
- W4280510305 hasConcept C62520636 @default.
- W4280510305 hasConceptScore W4280510305C114614502 @default.
- W4280510305 hasConceptScore W4280510305C118615104 @default.
- W4280510305 hasConceptScore W4280510305C121332964 @default.
- W4280510305 hasConceptScore W4280510305C132525143 @default.
- W4280510305 hasConceptScore W4280510305C158693339 @default.
- W4280510305 hasConceptScore W4280510305C180356752 @default.
- W4280510305 hasConceptScore W4280510305C33923547 @default.
- W4280510305 hasConceptScore W4280510305C62520636 @default.
- W4280510305 hasLocation W42805103051 @default.
- W4280510305 hasOpenAccess W4280510305 @default.
- W4280510305 hasPrimaryLocation W42805103051 @default.
- W4280510305 hasRelatedWork W1573315184 @default.
- W4280510305 hasRelatedWork W1964076852 @default.
- W4280510305 hasRelatedWork W2058863301 @default.
- W4280510305 hasRelatedWork W2099528956 @default.
- W4280510305 hasRelatedWork W2105981200 @default.
- W4280510305 hasRelatedWork W2952583369 @default.
- W4280510305 hasRelatedWork W2962841258 @default.
- W4280510305 hasRelatedWork W3132233781 @default.
- W4280510305 hasRelatedWork W3193859697 @default.
- W4280510305 hasRelatedWork W4280510305 @default.
- W4280510305 isParatext "false" @default.
- W4280510305 isRetracted "false" @default.
- W4280510305 workType "article" @default.