Harmony Morris
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View article: On the singular pebbling number of a graph
On the singular pebbling number of a graph Open
In this paper, we define a new parameter of a graph as a spin-off of the pebbling number (which is the smallest $t$ such that every supply of $t$ pebbles can satisfy every demand of one pebble). This new parameter is the singular pebbling …
View article: On generalised Petersen graphs of girth 7 that have cop number 4
On generalised Petersen graphs of girth 7 that have cop number 4 Open
We show that if $n=7k/i$ with $i \in \{1,2,3\}$ then the cop number of the generalised Petersen graph $GP(n,k)$ is $4$, with some small previously-known exceptions. It was previously proved by Ball et al. (2015) that the cop number of any …