arXiv subjects
Publications and source records attributed to Adrian Riskin.
We prove that $K_{n}$ is $\mathbb{Z}_{2}^{2}$-cordial if and only if $1 \leq n \leq 3$ and that $K_{m,n}$ is $\mathbb{Z}_{2}^{2}$ if and only if it is false that $m=n=2$.
We describe a new system for the simulation of simultaneous moves between noncolocational players. This has applications in the burgeoning Rock-Paper-Scissors by mail movement.
We calculate the cordial edge deficiencies of the complete multipartite graphs and find an upper bound for their cordial vertex deficiencies. We also give conditions under which the tensor product of two cordial graphs is cordial.
We develop a quite elementary graph theoretic system for designing small-size augmented origami polyhedra out of Sonobé modules beginning with a (convex or not) deltahedron.
We calculate exact values of the decycling numbers of $C_{m} \times C_{n}$ for $m=3,4$, of $C_{n}^{2}$, and of $C_{n}^{3}$.
We introduce two new measures of the noncordiality of a graph. We then calculate the values of these measures for various families of noncordial graphs. We also determine exactly which of the Möbius ladders are cordial.
In answer to a question of Eggleton, we prove that the complete multigraph on 5 vertices with edge multiplicity 6, namely $K_{5}^{(6)}$, has a decomposition into 5 copies of the family of trees of order 5 and that $K_{7}^{(22)}$ has a decomposition into 7 copies of the family of trees of order 7. We prove something similar for $K_{2n+1}$ for $n \le 13$.
We calculate the outerplanar crossing numbers of complete multipartite graphs which have $n$ partite sets with $m$ vertices and one partite set with $p$ vertices, where either $p|mn$ or $mn|p$.
We prove that if $G$ is a $2r$-regular edge graceful $(p,q)$ graph with $(r,kp)=1$ then $kG$ is edge graceful for odd $k$. We also prove that for certain specific classes of $2r$-regular edge graceful graphs it is possible to drop the requirement that $(r,kp)=1$
We define a new kind of crossing number which generalizes both the bipartite crossing number and the outerplanar crossing number. We calculate exact values of this crossing number for many complete bipartite graphs and also give a lower bound.