拓扑指标

数学表达式

Wiener

$W\left(G_{sw}\right)={\displaystyle \sum _{\left\{u,v\right\}\subseteq V\left(G_{sw}\right)}}{w}_v\left(u\right)w_v\left(v\right)d_{G_{sw}}\left(u,v\right)$

Edge-Wiener

$\begin{array}{c}{W}_e\left(G_{sw}\right)={\displaystyle \sum _{\left\{u,v\right\}\subseteq V\left(G_{sw}\right)}}{s}_v\left(u\right)s_v\left(v\right)d_{G_{sw}}\left(u,v\right)\\ +{\displaystyle \sum _{\left\{e,f\right\}\subseteq E\left(G_{sw}\right)}}{s}_e\left(e\right)s_e\left(f\right)D_{G_{sw}}\left(e,f\right)\\ +{\displaystyle \sum _{u\in V\left(G_{sw}\right)}}{\displaystyle \sum _{f\in E\left(G_{sw}\right)}}{s}_v(u)s_e\left(f\right)d_{G_{sw}}\left(u,f\right)\end{array}$

Vertex-edge-Wiener

$\begin{array}{l}{W}_{ve}\left(G_{sw}\right)=\frac{1}{2}[{\displaystyle \sum _{\left\{u,v\right\}\subseteq V\left(G_{sw}\right)}}\left\{w_v\left(u\right)s_v\left(v\right)+w_v\left(v\right)s_v\left(u\right)\right\}{d}_{G_{sw}}\left(u,v\right)\\ +{\displaystyle \sum _{u\in V\left(G_{sw}\right)}}{\displaystyle \sum _{f\in E\left(G_{sw}\right)}}{w}_v\left(u\right)s_e\left(f\right)d_{G_{sw}}\left(u,f\right)]\end{array}$

Vertex-Szeged

$S{z}_v\left(G_{sw}\right)={\displaystyle \sum _{e\mathrm{<mo>\; =\; </mo>}uv\in E\left(G_{sw}\right)}}{s}_e\left(e\right)n_u\left(e\mathrm{<mo>\; |\; </mo>}{G}_{sw}\right)n_v\left(e\mathrm{<mo>\; |\; </mo>}{G}_{sw}\right)$

Edge-Szeged

$S{z}_e\left(G_{sw}\right)={\displaystyle \sum _{e=uv\in E\left(G_{sw}\right)}}{s}_e\left(e\right)m_u\left(e\mathrm{<mo>\; |\; </mo>}{G}_{sw}\right)m_v\left(e\mathrm{<mo>\; |\; </mo>}{G}_{sw}\right)$

Edge-vertex-Szeged

$S{z}_{ev}\left(G_{sw}\right)=\frac{1}{2}{\displaystyle \sum _{e=uv\in E\left(G_{sw}\right)}}{s}_e\left(e\right)\left[n_u\left(e|G_{sw}\right)m_v\left(e|G_{sw}\right)+n_v\left(e|G_{sw}\right)m_u\left(e|G_{sw}\right)\right]$

Total-Szeged

$S{z}_t\left(G_{sw}\right)=S{z}_v\left(G_{sw}\right)+S{z}_e\left(G_{sw}\right)+2S{z}_{ev}\left(G_{sw}\right)$

Padmakar-Ivan

$PI\left(G_{sw}\right)={\displaystyle \sum _{e\mathrm{<mo>\; =\; </mo>}uv\in E\left(G_{sw}\right)}}{s}_e\left(e\right)\left[m_u\left(e\mathrm{<mo>\; |\; </mo>}{G}_{sw}\right)+m_v\left(e\mathrm{<mo>\; |\; </mo>}{G}_{sw}\right)\right]$

Schultz

$S\left(G_{sw}\right)\mathrm{<mo>\; =\; </mo>}{\displaystyle \sum _{\left\{u,v\right\}\subseteq V\left(G_{sw}\right)}}\left[w_v\left(v\right)d_{G_{sw}}\left(u\right)+w_v\left(u\right)d_{G_{sw}}\left(v\right)\right]d_{G_{sw}}\left(u\mathrm{,}v\right)$

Gutman

$Gut\left(G_{sw}\right)={\displaystyle \sum _{\left\{u,v\right\}\subseteq V\left(G_{sw}\right)}}{d}_{G_{sw}}\left(u\right)d_{G_{sw}}\left(v\right)d_{G_{sw}}\left(u\mathrm{,}v\right)$

Mostar

$Mo\left(G_{sw}\right)={\displaystyle \sum _{e=uv\in E\left(G_{sw}\right)}}{s}_e\left(e\right)\left|n_u\left(e\mathrm{<mo>\; |\; </mo>}{G}_{sw}\right)-n_v\left(e\mathrm{<mo>\; |\; </mo>}{G}_{sw}\right)\right|$

Edge-Mostar

$M{o}_e\left(G_{sw}\right)={\displaystyle \sum _{e=uv\in E\left(G_{sw}\right)}}{s}_e\left(e\right)\left|m_u\left(e|G_{sw}\right)-m_v\left(e|G_{sw}\right)\right|$

Total-Mostar

$M{o}_t\left(G_{sw}\right)={\displaystyle \sum _{e=uv\in E\left(G_{sw}\right)}}{s}_e\left(e\right)\left|t_u\left(e|G_{sw}\right)-t_v\left(e|G_{sw}\right)\right|$