Edge Version of Harmonic Index and Harmonic Polynomial of Some Classes of Graphs

Nazir, Rabia; Sardar, Muhammad Shoaib; Zafar, Sohail; Zahid, Zohaib

doi:10.14317/jami.2016.479

Cited by 8 publications

(9 citation statements)

References 11 publications

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“…x d u +d v −1 , and the harmonic polynomials of some graphs are computed. The harmonic polynomials of the line of some graphs are computed in reference [21]. This polynomial owes its name to the fact that 2 1 0 H(G, x) dx = H(G).…”

Section: Introductionmentioning

confidence: 99%

f-Polynomial on Some Graph Operations

et al. 2019

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Given any function f : Z + → R + , let us define the f-index I f ( G ) = ∑ u ∈ V ( G ) f ( d u ) and the f-polynomial P f ( G , x ) = ∑ u ∈ V ( G ) x 1 / f ( d u ) − 1 , for x > 0 . In addition, we define P f ( G , 0 ) = lim x → 0 + P f ( G , x ) . We use the f-polynomial of a large family of topological indices in order to study mathematical relations of the inverse degree, the generalized first Zagreb, and the sum lordeg indices, among others. In this paper, using this f-polynomial, we obtain several properties of these indices of some classical graph operations that include corona product and join, line, and Mycielskian, among others.

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Section: Introductionmentioning

confidence: 99%

f-Polynomial on Some Graph Operations

et al. 2019

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“…Several graph parameters have been used to define a graph polynomial, for instance, differential number, the parameters associated to matching, independent and domination sets, chromatic numbers and many others (see, e.g., [12] and the references therein). In recent years there have been many works on graph polynomials associated with different topological indices (see, e.g., [13][14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

“…The harmonic polynomials of the line graphs were studied in [17]. The inverse degree polynomial is studied to understand better the inverse degree topological index.…”

Section: Introductionmentioning

confidence: 99%

On the Inverse Degree Polynomial

et al. 2019

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“…x d u +d v −1 , and the harmonic polynomials of some graphs are computed. For more information on the study of polynomials associated with topological indices and their practical applications, see, e.g., [20][21][22][23]. This polynomial owes its name to the fact that 2 1 0 H(G, x) dx = H(G).…”

Section: Introductionmentioning

confidence: 99%

Harmonic Index and Harmonic Polynomial on Graph Operations

et al. 2018

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Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, corona product, join, Cartesian sum and lexicographic product. Some upper and lower bounds for the harmonic indices of these operations of graphs, in terms of related indices, are derived from known bounds on the integral of a product on nonnegative convex functions. Besides, we provide an algorithm that computes the harmonic polynomial with complexity O ( n 2 ) .

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Edge Version of Harmonic Index and Harmonic Polynomial of Some Classes of Graphs

Abstract: In this paper we define the edge version of harmonic index and harmonic polynomial of a graph G. We computed explicit formulas for the edge version of harmonic index and harmonic polynomial of many well known classes of graphs.

Cited by 8 publications

References 11 publications

f-Polynomial on Some Graph Operations

f-Polynomial on Some Graph Operations

On the Inverse Degree Polynomial

Harmonic Index and Harmonic Polynomial on Graph Operations

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