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On the general sum-connectivity index and general Randić index of cacti
oleh: Shehnaz Akhter, Muhammad Imran, Zahid Raza
Format: | Article |
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Diterbitkan: | SpringerOpen 2016-11-01 |
Deskripsi
Abstract Let G be a connected graph. The degree of a vertex x of G, denoted by d G ( x ) $d_{G}(x)$ , is the number of edges adjacent to x. The general sum-connectivity index is the sum of the weights ( d G ( x ) + d G ( y ) ) α $(d_{G}(x)+d_{G}(y))^{\alpha}$ for all edges xy of G, where α is a real number. The general Randić index is the sum of weights of ( d G ( x ) d G ( y ) ) α $(d_{G}(x)d_{G}(y))^{\alpha}$ for all edges xy of G, where α is a real number. The graph G is a cactus if each block of G is either a cycle or an edge. In this paper, we find sharp lower bounds on the general sum-connectivity index and general Randić index of cacti.