.png){kind=icon}
.png){kind=icon}
Return
Distribution eigenvalues and temperature index of graphs
.png){kind=icon}
OA
AI
DOI：10.1515/spma-2025-0045.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Let G be a simple graph on n n vertices with degree sequence d(1) , & mldr; , d(n) . Fajtlowicz (On conjectures of Graffiti, Discrete Math. 72 (1988), 113-118) defined the temperature of a vertex v of G G as d /n - d, where d is the degree of v . Motivated by this definition, we define the temperature index of G , denoted by T( G ), as T( G ) = d(1)/ n - d(1) + & ctdot; + dn/ n - d(n). We obtain some lower bounds and upper bounds for T ( G ) in terms of the number of vertices, the number of edges, the maximum and the minimum vertex degree and the Zagreb index ( Z ( G ) = d ( 2)(1) + & ctdot; + d (n) (2) . Using these results we derive new bounds for the Zagreb index of graphs. Finally, we study the temperature index of graphs from the point of view of spectra of graphs (the eigenvalues of their adjacency matrices). In particular, we show that G G has at least one eigenvalue in the interval [ - root n - delta root T ( G ) - 2 m/ n , root n - delta T ( G ) - 2 m/ n ].
Keywords:
temperature index
eigenvalues of graphs
spectral radius
Zagreb index
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.