Comparing the Zagreb indices of the NEPS of graphs

Stevanović, Dragan

doi:10.1016/j.amc.2012.07.014

Cited by 4 publications

(5 citation statements)

References 7 publications

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“…□ Corollary 1 (see [32]). We proceed further to describe an upper bound of the zeroth-order general Randić index of NEPS graphs for c ∈ Z − .…”

Section: Discussion and Main Resultsmentioning

confidence: 93%

“…In 2012, Stevanoić [32] investigated the Zagreb indices for NEPS of graphs and showed that inequalities in conjecture M 1 (H)/|V| ≤ M 2 (H)/|E| unchanged under NEPS of graphs. In [33], the authors determined that the family of gcd-graphs and the family of NEPS of complete graphs coincide.…”

Section: Introductionmentioning

confidence: 99%

“…For a more detailed study of NEPS and related topics, we refer the reader to [34][35][36][37][38][39][40][41]. In this paper, we extended the results of Stevanoić [32] and investigated the formulas of well-known degree-related topological descriptors for the NEPS of graphs.…”

Section: Introductionmentioning

confidence: 99%

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Computation of Topological Indices of NEPS of Graphs

2021

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The inspection of the networks and graphs through structural properties is a broad research topic with developing significance. One of the methods in analyzing structural properties is obtaining quantitative measures that encode data of the whole network by a real quantity. A large quantity of graph-associated numerical invariants has been used to examine the whole structure of networks. In this analysis, degree-related topological indices have a significant place in nanotechnology and theoretical chemistry. Thereby, the computation of indices is one of the successful branches of research. The noncomplete extended p -sum NEPS of graphs is a famous general graph product. In this paper, we investigated the exact formulas of general zeroth-order Randić, Randić, and the first multiplicative Zagreb indices for NEPS of graphs.

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“…□ Corollary 1 (see [32]). We proceed further to describe an upper bound of the zeroth-order general Randić index of NEPS graphs for c ∈ Z − .…”

Section: Discussion and Main Resultsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Computation of Topological Indices of NEPS of Graphs

2021

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“…Soon after the inequality was announced, it was investigated in [12] that there exist graphs for which (1) fails to hold. Despite of the fact that the work presented in [12] seemed to completely resolve Hansen's conjecture, it was just the origin of a novel platform for researchers to investigate the validity or non-validity of (1) for numerous classes of graphs [1][2][3]6,8,11,[14][15][16][20][21][22]24]. The developments on this conjecture are summarized in the survey [18].…”

Section: Although Thementioning

confidence: 99%

More on the Zagreb indices inequality

Nadeem¹,

Siddique²

2021

match

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The Zagreb indices are very popular topological indices in mathematical chemistry and attracted a lot of attention in recent years. The first and second Zagreb indices of a graph G = (V, E) are defined as M 1 (G) = vi∈V d 2 ı and M 2 (G) = υi∼υȷ (didȷ), where di denotes the degree of a vertex υi and υi ∼ υȷ represents the adjacency of vertices υi and υȷ in G. It has been conjectured that M 1 /n ≤ M 2 /m holds for a connected graph G with n = |V | and m = |E|. Later, it is proved that this inequality holds for some classes of graphs but does not hold in general. This inequality is proved to be true for graphs with di ∈, where h ≥ z(z − 1)/2. In this paper, we prove that the graphs satisfy the inequality if the sequences (di) and (Si) have the similar monotonicity, where Si = υȷ∈N (υi) dȷ and N (υi) = {υȷ ∈ V |υi ∼ υȷ}. As a consequence, we present an infinite family of connected graphs with di ∈ [1, ∞), for which the inequality holds. Moreover, we establish the relations between M 1 /n and M 2 /m in case of general graphs.

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“…Weiner-Index [12] is one of the earliest topological indices introduced by Weiner in connection with modeling of organic molecules in Chemistry. Several such indices (see, for example, [5,8] ) have been introduced and investigated subsequently. The eccentric connectivity index is a parameter recently introduced [10] and subsequently studied (see for example [2,6,7,11,13]) with regard to physical / biological properties of molecules.…”

Section: Introductionmentioning

confidence: 99%

On Eccentric Connectivity Index of Eccentric Graph of Regular Dendrimer

Nagar

Sriram

2016

Math.Comput.Sci.

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Abstract. The eccentric connectivity index ξ c (G) of a connected graphis the degree of vertex v and e(v) is the eccentricity of v. The eccentric graph Ge of a graph G has the same set of vertices as G, with two vertices u, v adjacent in Ge if and only if either u is an eccentric vertex of v or v is an eccentric vertex of u. In this paper, we obtain a formula for the eccentric connectivity index of the eccentric graph of a regular dendrimer. We also derive a formula for the eccentric connectivity index for the second iteration of eccentric graph of regular dendrimer.

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Comparing the Zagreb indices of the NEPS of graphs

Cited by 4 publications

References 7 publications

Computation of Topological Indices of NEPS of Graphs

Computation of Topological Indices of NEPS of Graphs

More on the Zagreb indices inequality

On Eccentric Connectivity Index of Eccentric Graph of Regular Dendrimer

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