Scopus
YÖKSİS Eşleşti
Laplacian coefficients, Kirchhoff index and the number of spanning trees of graphs
Asian-European Journal of Mathematics · Nisan 2024
YÖKSİS Kayıtları
Laplacian coefficients, Kirchhoff index and the number of spanning trees of graphs
Asian-European Journal of Mathematics · 2024 ESCI
PROFESÖR ŞERİFE BURCU BOZKURT ALTINDAĞ →
Makale Bilgileri
DergiAsian-European Journal of Mathematics
Yayın TarihiNisan 2024
Cilt / Sayfa17
Scopus ID2-s2.0-85190116200
Özet
Let G = (V, E), V = {v1 , v2, . . ., vn}, be a simple connected graph of order n and size m. Denote with μ1 ≥ μ2 ≥ · · · ≥ μn−1 > μn = 0 eigenvalues of the Laplacian matrix L(G) of G. The Kirchhoff index and the number of spanning trees of G expressed in terms of Laplacian eigenvalues are given by Kf (G) = n Pni=1−1 1 µi and t(G) = n1 Qni=1−1 μi, respectively. The characteristic polynomial of L(G) is given by φ(L(G)) = Pnk=0 pkxn−k. The first five Laplacian coefficients have been computed in the literature. In this study, we compute the sixth Laplacian coefficient of G. Then, we use it to improve the previously obtained results on Kf(G) and t(G). In addition, we present new Nordhaus–Gaddumtype inequalities for Kf(G) and t(G).
Yazarlar (3)
1
B.Bozkurt Altındag
ORCID: 0009-0003-3185-886X
2
I. Milovanović
ORCID: 0000-0003-2209-9606
3
E. Milovanović
ORCID: 0000-0002-1905-4813
Anahtar Kelimeler
Kirchhoff index
Laplacian coefficients
Laplacian eigenvalues
spanning tree
Kurumlar
Selçuk Üniversitesi
Selçuklu Turkey
University of Niš
Nis Serbia