arXiv subjects
Publications and source records attributed to Penying Rochanakul.
A weak homomorphism from a graph G to a graph H is a mapping f from V(G) to V(H), where either f(x) = f(y) or {f(x), f(y)} is an element of E(H), and this holds for all {x, y} in E(G). A rectangular grid graph is formed by taking the Cartesian product of two paths. In this paper, we present a formula for calculating the number of weak homomorphisms from paths to rectangular grid graphs.
A finite, simple and undirected graph $G = (V, E)$ with $p$ vertices and $q$ edges is said to be a $k$-geometric mean graph for a positive integer $k$ if there is an injection $ψ:V(G)\to \{k,k+1,\dots,k+q\}$ such that, when each edge $uv\in E(G)$ is assigned the label $\lfloor\sqrt{ψ(u)ψ(v)}\rfloor$ or $\lceil\sqrt{ψ(u)ψ(v)}\rceil$, the resulting edge label set is $\{k,k+1,...,k+q-1\}$ and $ψ$ is called a \emph{$k$-geometric mean labeling} of $G$. The special case $k=1$, a $1$-geometric mean labeling is called a geometric mean labeling, and a $1$-geometric mean graph is called a geometric mean graph. In this paper, we present new classes of geometric mean graphs. Then we introduce $k$-geometric mean labeling and prove some classes of graphs are $k$-geometric mean. We also study some classes of finite join of graphs that admit geometric mean labeling.
We extend the concept of two-level fingerprinting codes, introduced by Anthapadmanabhan and Barg (2009) in context of traceability (TA) codes, to other types of fingerprinting codes, namely identifiable parent property (IPP) codes, secure-frameproof (SFP) codes, and frameproof (FP) codes. We define and propose the first explicit non-trivial construction for two-level IPP, SFP and FP codes.