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Please let me know if the following graphs popped up in some problems.

Each of these graphs is described by 5 integers $n_1\geqslant k_1$, $n_2\geqslant k_2$, $l\geqslant 0$. We take two complete graphs $K_{n_1}$ and $K_{n_2}$ and a path $P_l$ of length $l$, the left endvertex of $P_l$ is connected to $k_1$ vertices of $K_{n_1}$ and and the right endvertex of $P_l$ is connected to $k_2$ vertices of $K_{n_2}$. In addition we assume that if $n_i>0$ then $k_i>0$, so the obtained graph is connected.

Here three examples for

• $n_1=4,k_1=2,l=3,k_2=2,n_2=4$;
• $n_1=4,k_1=2,l=0,k_2=0,n_2=0$;
• $n_1=2,k_1=2,l=0,k_2=2,n_2=2$.

These graphs encode solutions of certain problem in metric geometry related to the so-called graph comparison.

Please let me know if the following graphs popped up in some problems.

Each of these graphs is described by 5 integers $n_1\geqslant k_1$, $n_2\geqslant k_2$, $l\geqslant 0$. We take two complete graphs $K_{n_1}$ and $K_{n_2}$ and a path $P_l$ of length $l$, the left endvertex of $P_l$ is connected to $k_1$ vertices of $K_{n_1}$ and and the right endvertex of $P_l$ is connected to $k_2$ vertices of $K_{n_2}$. In addition we assume that if $n_i>0$ then $k_i>0$, so the obtained graph is connected.

Here three examples for

• $n_1=4,k_1=2,l=3,k_2=2,n_2=4$;
• $n_1=4,k_1=2,l=0,k_2=0,n_2=0$;
• $n_1=2,k_1=2,l=0,k_2=2,n_2=2$.

These graphs encode solutions of certain problem in metric geometry related to the so-called graph comparison.

Please let me know if the following graphs popped up in some problems.

Each of these graphs is described by 5 integers $n_1\geqslant k_1$, $n_2\geqslant k_2$, $l\geqslant 0$. We take two complete graphs $K_{n_1}$ and $K_{n_2}$ and a path $P_l$ of length $l$, the left endvertex of $P_l$ is connected to $k_1$ vertices of $K_{n_1}$ and and the right endvertex of $P_l$ is connected to $k_2$ vertices of $K_{n_2}$. In addition we assume that if $n_i>0$ then $k_i>0$, so the obtained graph is connected.

Here some examples:

These graphs encode solutions of certain problem in metric geometry related to the so-called graph comparison.

Please let me know if the following graphs popped up in some problems.

Each of these graphs is described by 5 integers $n_1\geqslant k_1$, $n_2\geqslant k_2$, $l\geqslant 0$. We take two complete graphs $K_{n_1}$ and $K_{n_2}$ and a path $P_l$ of length $l$, the left endvertex of $P_l$ is connected to $k_1$ vertices of $K_{n_1}$ and and the right endvertex of $P_l$ is connected to $k_2$ vertices of $K_{n_2}$. In addition we assume that if $n_i>0$ then $k_i>0$, so the obtained graph is connected.

Here three examples for

• $n_1=4,k_1=2,l=3,k_2=2,n_2=4$;
• $n_1=4,k_1=2,l=0,k_2=0,n_2=0$;
• $n_1=2,k_1=2,l=0,k_2=2,n_2=2$.

These graphs encode solutions of certain problem in metric geometry related to the so-called graph comparison.

Please let me know if the following graphs popped up in some problems.

Each of these graphs is described by 5 integers $n_1\geqslant k_1$, $n_2\geqslant k_2$, $l\geqslant 0$. We take two complete graphs $K_{n_1}$ and $K_{n_2}$ and a path $P_l$ of length $l$, the left endvertex of $P_l$ is connected to $k_1$ vertices of $K_{n_1}$ and and the right endvertex of $P_l$ is connected to $k_2$ vertices of $K_{n_2}$. In addition we assume that if $n_i>0$ then $k_i>0$, so the obtained graph is connected.

Here some examples:

These graphs encode solutions of certain problem in metric geometry related to the graph comparison introduced in our paper.

Please let me know if the following graphs popped up in some problems.

Each of these graphs is described by 5 integers $n_1\geqslant k_1$, $n_2\geqslant k_2$, $l\geqslant 0$. We take two complete graphs $K_{n_1}$ and $K_{n_2}$ and a path $P_l$ of length $l$, the left endvertex of $P_l$ is connected to $k_1$ vertices of $K_{n_1}$ and and the right endvertex of $P_l$ is connected to $k_2$ vertices of $K_{n_2}$. In addition we assume that if $n_i>0$ then $k_i>0$, so the obtained graph is connected.

Here some examples:

These graphs encode solutions of certain problem in metric geometry related to the so-called graph comparison.