‎the harmonic index of a connected graph $g$‎, ‎denoted by $h(g)$‎, ‎is‎ ‎defined as $h(g)=sum_{uvin e(g)}frac{2}{d_u+d_v}$‎ ‎where $d_v$ is the degree of a vertex $v$ in g‎. ‎in this paper‎, ‎expressions for the harary indices of the‎ ‎join‎, ‎corona product‎, ‎cartesian product‎, ‎composition and symmetric difference of graphs are‎ ‎derived‎.

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The use of silicon carbide is increasing significantly in the fields research and technology. Topological indices enable data gathering on algebraic graphs provide a mathematical framework for analyzing chemical structural characteristics. In this paper, well-known degree-based topological are used to analyze structures carbides. To evaluate features various or non-chemical networks, variety de...

the fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. in this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. so ,  a novel method for computing the new descriptors to construct a quantitative rela...

abstract. topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. graph theory is a delightful playground for the exploration of proof techniques in discrete mathematics and its results have applications in many areas of sciences. a graph is a ...

abstract. topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. graph theory is a delightful playground for the exploration of proof techniques in discrete mathematics and its results have applications in many areas of sciences. one of the us...

The degeneracy of topological distance sum (DS) and distance degree sequence (DDS) of small fullerenes is analyzed. The degeneracy of the two topological descriptors is determined by comparing the topological equivalence classes of the fullerene atoms with the DS and DDS classes, respectively. On the basis of DS and DDS degenerated fullerene graphs and by using two previously demonstrated theor...

The purpose of this study was to evaluate the moderate term (5 weeks) reproducibility of Borg scale ratings of the effort to breathe (Borge) and the degree of discomfort evoked by breathing (Borgd) in patients with COPD during exercise. Six subjects with moderately severe COPD (FEV1, 1.42 +/- 0.50 L) underwent progressive incremental exercise (15 W/min) on a cycle ergometer to a symptom-limited...