Yazar "Das, Kinkar Ch" seçeneğine göre listele

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  • Küçük Resim
    Öğe
    On Kirchhoff Index and Resistance-Distance Energy of a Graph
    (Univ Kragujevac, Fac Science, 2012) Das, Kinkar Ch; Güngör, A. Dilek; Çevik, A. Sinan
    We report lower hounds for the Kirchhoff index of a connected (molecular) graph in terms of its structural parameters such as the number of vertices (atoms), the number of edges (bonds), maximum vertex degree (valency), second maximum vertex degree and minimum vertex degree. Also we give the Nordhaus-Gaddum-type result for Kirchhoff index. In this paper we define the resistance distance energy as the sum of the absolute values of the eigenvalues of the resistance distance matrix and also we obtain lower and upper bounds for this energy.
  • Küçük Resim Yok
    Öğe
    On the first Zagreb index and multiplicative Zagreb coindices of graphs
    (OVIDIUS UNIV PRESS, 2016) Das, Kinkar Ch; Akgüneş, Nihat; Togan, Müge; Yurttaş, Aysun; Cangül, I. Naci; Çevik, A. Sinan
    For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M-1(G) = Sigma v(i is an element of V(G))d(C)(v(i))(2), where d(G) (v(i)) is the degree of vertex v(i), in G. Recently Xu et al. introduced two graphical invariants (Pi) over bar (1) (G) = Pi v(i)v(j is an element of E(G)) (dG (v(i))+dG (v(j))) and (Pi) over bar (2)(G) = Pi(vivj is an element of E(G)) (dG (v(i))+dG (v(j))) named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = Pi(n)(i=1) d(G) (v(i)). The irregularity index t(G) of G is defined as the num=1 ber of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M-1(G) of graphs and trees in terms of number of vertices, irregularity index, maximum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and NarumiKatayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.