Some inequalities for general zeroth-order Randic index

Let G = (V, E), V = {v1, v2,..., vn}, be a simple graph without isolated vertices, with the sequence of vertex degrees d1 ? d2 ?...? dn > 0, di = d(vi). If vertices vi and vj are adjacent in G, we write i ~ j, otherwise we write i ~/ j. The inverse degree topological index of G is defined to be ID(G) = ?ni=1 1/di = ? i~j (1/d2i + 1/d2j), and the inverse degree coindex ?ID(G) = ? i~/j(1/d2i + 1/d2j). We obtain a number of inequalities which determine bounds for the ID(G) and ?ID(G) when G is a tree.

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“…from which the inequality ( 6) is obtained. Equality in (10), and hence in (6), holds if T is a tree with the property…”

Section: Resultsmentioning

confidence: 99%

Some properties of the inverse degree index and coindex of trees

Mitić

Milovanovic

Matejic

et al. 2022

Filomat

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“…Equality holds if and only if G ∼ = n 2 K 2 , for even n. Proof. In [22] it was proven that for any real α and β holds…”

Section: Equality Holds If and Only Ifmentioning

confidence: 99%

McClelland-Type Upper Bounds for Graph Energy

Milovanovic¹,

Milovanovic²,

Matejic³

2022

Match

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“…• Equation (1) gives the general zeroth-order Randić index if f (x) = x α (see for example [14][15][16][17][18]), where α is a real number.…”

Section: Introductionmentioning

confidence: 99%

On the Vertex-Degree-Function Indices of Connected (n,m)-Graphs of Maximum Degree at Most Four

Albalahi¹,

Milovanovic²,

Raza³

et al. 2022

Preprint

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Consider a graph G and a real-valued function f defined on the degree set of G. The sum of the outputs f (d v ) over all vertices v ∈ V (G) of G is usually known as the vertex-degreefunction indices and is denoted by H f (G), where d v represents the degree of a vertex v of G. This paper gives sharp bounds on the index H f (G) in terms of order and size of G when G is connected and has the maximum degree at most 4. All the graphs achieving the derived bounds are also determined. Bounds involving several existing indices -including the general zeroth-order Randić index and coindex, the general multiplicative first/second Zagreb index, the variable sum lodeg index, the variable sum exdeg index -are deduced as the special cases of the obtained ones.

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Some inequalities for general zeroth-order Randic index

Cited by 7 publications

References 12 publications

Some properties of the inverse degree index and coindex of trees

Some properties of the inverse degree index and coindex of trees

McClelland-Type Upper Bounds for Graph Energy

On the Vertex-Degree-Function Indices of Connected (n,m)-Graphs of Maximum Degree at Most Four

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