Four new operations related to composition and their reformulated Zagreb index
نویسندگان
چکیده
منابع مشابه
Reformulated First Zagreb Index of Some Graph Operations
The reformulated Zagreb indices of a graph are obtained from the classical Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of the end vertices of the edge minus 2. In this paper, we study the behavior of the reformulated first Zagreb index and apply our results to different chemically interesting molecular graphs and nano-...
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The first general Zagreb index is defined as $M_1^lambda(G)=sum_{vin V(G)}d_{G}(v)^lambda$. The case $lambda=3$, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as $EM_1^lambda(G)=sum_{ein E(G)}d_{G}(e)^lambda$ and the reformulated F-index is $RF(G)=sum_{ein E(G)}d_{G}(e)^3$. In this paper, we compute the reformulated F-index for some grap...
متن کاملThe Hyper-Zagreb Index of Four Operations on Graphs
The hyper-Zagreb index of a connected graph G, denoted by HM(G), is defined as HM(G) = ∑ uv∈E(G) [dG(u) + dG(v)] where dG(z) is the degree of a vertex z in G. In this paper, we study the hyper-Zagreb index of four operations on graphs.
متن کاملThe Hyper-Zagreb Index of Graph Operations
Let G be a simple connected graph. The first and second Zagreb indices have been introduced as vV(G) (v)2 M1(G) degG and M2(G) uvE(G)degG(u)degG(v) , respectively, where degG v(degG u) is the degree of vertex v (u) . In this paper, we define a new distance-based named HyperZagreb as e uv E(G) . (v))2 HM(G) (degG(u) degG In this paper, the HyperZagreb index of the Cartesian p...
متن کاملOn the Bounds of the First Reformulated Zagreb Index
The edge version of traditional first Zagreb index is known as first reformulated Zagreb index. In this paper, we analyze and compare various lower and upper bounds for the first reformulated Zagreb index and we propose new lower and upper bounds which are stronger than the existing and recent results [Appl. Math. Comp. 273 (2016) 16-20]. In addition, we prove that our bounds are superior in co...
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ژورنال
عنوان ژورنال: Indonesian Journal of Combinatorics
سال: 2018
ISSN: 2541-2205
DOI: 10.19184/ijc.2018.2.1.5