Some classes of dispersible dcsl-graphs
Journal Title: Карпатські математичні публікації - Year 2017, Vol 9, Issue 2
Abstract
A distance compatible set labeling dcsl of a connected graph G is an injective set assignment $f : V(G) \rightarrow 2^{X},$ $X$ being a non empty ground set, such that the corresponding induced function $f^{\oplus} :E(G) \rightarrow 2^{X}\setminus \{\phi\}$ given by $f^{\oplus}(uv)= f(u)\oplus f(v)$ satisfies $|f^{\oplus}(uv)| = k_{(u,v)}^{f}d_{G}(u,v) $ for every pair of distinct vertices $u, v \in V(G),$ where $d_{G}(u,v)$ denotes the path distance between u and v and $k_{(u,v)}^{f}$ is a constant, not necessarily an integer, depending on the pair of vertices u, v chosen. G is distance compatible set labeled dcsl graph if it admits a dcsl. A dcsl f of a (p, q)-graph G is dispersive if the constants of proportionality $k^f_{(u,v)}$ with respect to $f, u \neq v, u, v \in V(G)$ are all distinct and G is dispersible if it admits a dispersive dcsl. In this paper, we prove that all paths and graphs with diameter less than or equal to 2 are dispersible.
Authors and Affiliations
J. Jinto, K. A. Germina, P. Shaini
Keywords
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