Some eigenvalue properties in graphs (conjectures of Graffiti — II)

Favaron, Odile; Mahéo, Maryvonne; Saclé, Jean-François

doi:10.1016/0012-365x(93)90156-n

Cited by 213 publications

(113 citation statements)

References 7 publications

Supporting

Mentioning

106

Contrasting

Order By: Relevance

“…For α = − 1 2 from (17) 2R −1/2 ≤ n is obtained (see [14,25]). Closely related with this inequality is the irregularity measure for connected graphs proposed in [19] Now we mention some irregularity measures for line graphs that can be directly derived from the aforementioned inequalities.…”

Section: It Is Not Difficult To See That Irregularity Measures S(g) Amentioning

confidence: 99%

See 1 more Smart Citation

Irregularity measures of graph

Milovanovic¹,

Glogic²,

Milovanovic³

et al. 2015

Sci Publ State Univ Novi Pazar Ser A

View full text Add to dashboard Cite

show abstract

Section: It Is Not Difficult To See That Irregularity Measures S(g) Amentioning

confidence: 99%

“…We are interested in the case when α = − [34], whereas for α = 1 2 the reciprocal Randić index is obtained [14,26], i.e.…”

Section: Introductionmentioning

confidence: 99%

Irregularity measures of graph

Milovanovic¹,

Glogic²,

Milovanovic³

et al. 2015

Sci Publ State Univ Novi Pazar Ser A

View full text Add to dashboard Cite

show abstract

“…The values of these indices often have close correlation with various properties (for example, the boiling point or surface pressure of a chemical compound) of the objects under consideration.See for instance [1,2,4,5,7,12] for some of such applications. Among them, a group of indices defined in terms of the degrees of adjacent vertices have been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Functions on adjacent vertex degrees of trees with given degree sequence

Wang

2014

Open Mathematics

View full text Add to dashboard Cite

Abstract:In this note we consider a discrete symmetric function ( ) whereassociated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined asare characterized by the "greedy tree" and "alternating greedy tree". This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randić index follow as corollaries. The extremal structures for the relatively new sum-connectivity index and harmonic index also follow immediately, some of these extremal structures have not been identified in previous studies. MSC:05C05, 05C07, 05C35

show abstract

“…In [6], Favaron et al considered the relation between harmonic index and the eigenvalues of graphs. Zhong [7] found the minimum and maximum values of the harmonic index for connected graphs and trees, and characterized the corresponding extremal graphs.…”

Section: Introductionmentioning

confidence: 99%