- Tytuł:
- Signed Complete Graphs with Maximum Index
- Autorzy:
-
Akbari, Saieed
Dalvandi, Soudabeh
Heydari, Farideh
Maghasedi, Mohammad - Powiązania:
- https://bibliotekanauki.pl/articles/31530379.pdf
- Data publikacji:
- 2020-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
signed graph
complete graph
index - Opis:
- Let Γ = (G, σ) be a signed graph, where G is the underlying simple graph and σ E(G) → {−, +} is the sign function on the edges of G. The adjacency matrix of a signed graph has −1 or +1 for adjacent vertices, depending on the sign of the edges. It was conjectured that if is a signed complete graph of order n with k negative edges, k < n − 1 and has maximum index, then negative edges form K1,k. In this paper, we prove this conjecture if we confine ourselves to all signed complete graphs of order n whose negative edges form a tree of order k + 1. A [1, 2]-subgraph of G is a graph whose components are paths and cycles. Let Γ be a signed complete graph whose negative edges form a [1, 2]-subgraph. We show that the eigenvalues of Γ satisfy the following inequalities: −5 ≤ λn ≤ . . . ≤ λ2 ≤ 3.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 393-403
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł