On the first Zagreb index and multiplicative Zagreb coindices of graphs

Das, Kinkar Ch.; Akgüneş, Nihat; Togan, Muge; Yurttas, Aysun; Cangül, İsmaıl Nacı; Çevik, A. Sinan

doi:10.1515/auom-2016-0008

Cited by 37 publications

(31 citation statements)

References 15 publications

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“…We make the proof only for P r ∨ P s and S r ∨ C s . Let P r = 1 (2) , 2 (r−2) and P s = 1 (2) , 2 (s−2) .…”

Section: Algebraic Properties Of Joinmentioning

confidence: 99%

“…So their contribution is (r + 2) (s−2) . Therefore the required DS is P r ∨ P s = {(s + 1) (2) , (s + 2) (r−2) , (r + 1) (2) , (r + 2) (s−2) }.…”

Section: Algebraic Properties Of Joinmentioning

confidence: 99%

“…1. Introduction 1,2 Let G = (V (G), E(G)) be a simple and connected graph with | V (G) |= n vertices and | E(G) |= m edges. Usually we use the notations V and E instead of V (G) and E(G), respectively.…”

mentioning

confidence: 99%

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Algebraic Structure of Graph Operations in Terms of Degree Sequences

Mishra

Delen²,

Cangül³

2018

ijaa

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In this paper, by means of the degree sequences (DS) of graphs and some graph theoretical and combinatorial methods, we determine the algebraic structure of the set of simple connected graphs according to two graph operations, namely join and Corona product. We shall conclude that in the case of join product, the set of graphs forms an abelian monoid whereas in the case of Corona product, this set is not even associative, it only satisfies two conditions, closeness and identity element. We also give a result on distributive law related to these two operations.

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“…We make the proof only for P r ∨ P s and S r ∨ C s . Let P r = 1 (2) , 2 (r−2) and P s = 1 (2) , 2 (s−2) .…”

Section: Algebraic Properties Of Joinmentioning

confidence: 99%

“…So their contribution is (r + 2) (s−2) . Therefore the required DS is P r ∨ P s = {(s + 1) (2) , (s + 2) (r−2) , (r + 1) (2) , (r + 2) (s−2) }.…”

Section: Algebraic Properties Of Joinmentioning

confidence: 99%

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Algebraic Structure of Graph Operations in Terms of Degree Sequences

Mishra

Delen²,

Cangül³

2018

ijaa

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“…The extremal graphs with respect to was studied by Gutman and Ghorbani [15] , Zolfi and Ashrafi [20]. Some relations between the Narumi-Katayama index and the first Zagreb index were introduced in the more recent paper [21].…”

Section: = ( ) = ∑ Deg ( ) = ∑ (Deg( ) + Deg( ) ) ∈ ( ) ∈ ( )mentioning

confidence: 99%

On <em>ev</em>-degree and <em>ve</em>-degree topological indices

Şahin

Ediz

2017

Preprint

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Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the evdegree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we define the ve-degree and ev-degree Narumi-Katayama indices, investigate the predicting power of these novel indices and extremal graphs with respect to these novel topological indices. Also we give some basic mathematical properties of ev-degree and ve-degree NarumiKatayama and Zagreb indices.

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“…where E(G) represents the edge set of G. Till now, many papers have been devoted to these Zagreb indices, for example see the surveys [6][7][8], particularly the recent ones [9][10][11][12], the papers [13][14][15][16][17][18][19][20][21][22][23][24], and the related references cited therein.…”

Section: Introductionmentioning

confidence: 99%