Abstract

Recently, two novel degree based concepts have been defined in graph theory; $E_v$-degrees and $V_e$-degrees. Motivated by chemical applications of topological indices in the QSPR/QSAR analysis, we define $V_e$-degree re-defined versions of Zagreb indices ($V_e-ReZG_1(G)$, $V_e-ReZG_2(G)$, $V_e-ReZG_3(G)$) and $V_e$-degree of SK indices ($V_e-SK(G)$, $V_e-SK_1(G)$, $V_e-SK_2(G)$) as parallel to their corresponding classical degree versions. Further-more, we obtain $V_e$-degree $V_e-ReZG_1(G)$, $V_e-ReZG_2(G)$, $V_e-ReZG_3(G)$, $V_e-SK(G)$, $V_e-SK_1(G)$, $V_e-SK_2(G)$ and $E_v$-degree $E_v- {^{m}M(G)}$, $E_v-I(G)$, $E_v-F(G)$ of topological indices of some standard class of graphs like, path, cycle, complete, star, wheel and complete bipartite graphs. Also we compute $V_e-ReZG_1(G)$, $V_e-ReZG_2(G)$, $V_e-ReZG_3(G)$, $V_e-SK(G)$, $V_e-SK_1(G)$ and $V_e-SK_2(G)$ topological indices of some silicate oxygen networks such as dominating oxide network $(DOX)$, regular triangulate oxide network (RTOX), dominating silicate network (DSL) and derive analytical formulae of these networks. Additionally, we analyze the numerical and graphical comparison of the networks.

Keywords and Phrases

SK indices, re-defined Zagreb indices, $V_e$-degree and $E_v$-degree indices.

A.M.S. subject classification

05C05, 05C12, 05C35.

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