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A graph $G$ is stratified if its vertex set is partitioned into classes, called strata. If there are $k$ strata, then $G$ is $k$-stratified. These graphs were introduced to study problems in VLSI design. The strata in a stratified graph are also referred to as color classes. For a color $X$ in a stratified graph $G$, the $X$-eccentricity $e_X\left(v\right)$ of a vertex $v$ of $G$ is the distance between $v$ and an $X$-colored vertex furthest from $v$. The minimum $X$-eccentricity among the vertices of $G$ is the $X$-radius ${\mathrm{r}ad}_{X}G$ of $G$ and the maximum...

A graph $G$ is a stratified graph if its vertex set is partitioned into classes (each of which is a stratum or a color class). A stratified graph with $k$ strata is $k$-stratified. If $G$ is a connected $k$-stratified graph with strata $S_i$ $(1\le i\le k)$ where the vertices of $S_i$ are colored $X_i$ $(1\le i\le k)$, then the $X_i$-proximity ${\rho }_{X_i}\left(v\right)$ of a vertex $v$ of $G$ is the distance between $v$ and a vertex of $S_i$ closest to $v$. The strati-eccentricity $se\left(v\right)$ of $v$ is $max\{{\rho }_{X_i}\left(v\right)\mid 1\le i\le k\}$. The minimum strati-eccentricity over all vertices of $G$ is the...