On the first Zagreb index and multiplicative Zagreb coindices of graphs
نویسندگان
چکیده
منابع مشابه
Zagreb, multiplicative Zagreb Indices and Coindices of graphs
Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The first, second and third Zagreb indices of G are respectivly defined by: $M_1(G)=sum_{uin V} d(u)^2, hspace {.1 cm} M_2(G)=sum_{uvin E} d(u).d(v)$ and $ M_3(G)=sum_{uvin E}| d(u)-d(v)| $ , where d(u) is the degree of vertex u in G and uv is an edge of G connecting the vertices u and v. Recently, the first and second m...
متن کاملzagreb, multiplicative zagreb indices and coindices of graphs
let g=(v,e) be a simple connected graph with vertex set v and edge set e. the first, second and third zagreb indices of g are respectivly defined by: $m_1(g)=sum_{uin v} d(u)^2, hspace {.1 cm} m_2(g)=sum_{uvin e} d(u).d(v)$ and $ m_3(g)=sum_{uvin e}| d(u)-d(v)| $ , where d(u) is the degree of vertex u in g and uv is an edge of g connecting the vertices u and v. recently, the first and second m...
متن کاملMultiplicative Zagreb Indices and Coindices of Some Derived Graphs
In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.
متن کاملMore on Zagreb Coindices of Composite Graphs
For a nontrivial graph G, its first and second Zagreb coindices are defined [1], respectively, as M1(G) = ∑ uv ∈E(G) (dG(u)+dG(v)) and M2(G) = ∑ uv ∈E(G) dG(u)dG(v), where dG(x) is the degree of vertex x in G. In this paper, we obtained some new properties of Zagreb coindices. We mainly give explicit formulae for the first Zagreb coindex of line graphs and total graphs. Mathematics Subject Clas...
متن کاملMultiplicative Versions of First Zagreb Index
The first Zagreb index of a graph G, with vertex set V (G) and edge set E(G), is defined as M1(G) = ∑ u∈V (G) d(u) 2 where d(u) denotes the degree of the vertex v. An alternative expression for M1(G) is ∑ uv∈E(G)[d(u) + d(v)]. We consider a multiplicative version of M1 defined as Π∗1(G) = ∏ uv∈E(G)[d(u) + d(v)]. We prove that among all connected graphs with a given number of vertices, the path ...
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ژورنال
عنوان ژورنال: Analele Universitatii "Ovidius" Constanta - Seria Matematica
سال: 2016
ISSN: 1844-0835
DOI: 10.1515/auom-2016-0008