Some classes of dispersible dcsl-graphs
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...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2018-01-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1456 |
| _version_ | 1818240029571416064 |
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| author | J. Jinto K.A. Germina P. Shaini |
| author_facet | J. Jinto K.A. Germina P. Shaini |
| author_sort | J. Jinto |
| collection | DOAJ |
| description | 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 proved that all paths and graphs with diameter less than or equal to $2$ are dispersible. |
| first_indexed | 2024-12-12T13:06:57Z |
| format | Article |
| id | doaj.art-d4e66bc842f94a3cbdc0296cdfce9d43 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-12T13:06:57Z |
| publishDate | 2018-01-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-d4e66bc842f94a3cbdc0296cdfce9d432022-12-22T00:23:38ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102018-01-019212813310.15330/cmp.9.2.128-1331456Some classes of dispersible dcsl-graphsJ. Jinto0K.A. Germina1P. Shaini2Department of Mathematics, Central University of Kerala, Kasaragod, Kerala 671314, IndiaDepartment of Mathematics, Central University of Kerala, Kasaragod, Kerala 671314, IndiaDepartment of Mathematics, Central University of Kerala, Kasaragod, Kerala 671314, IndiaA 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 proved that all paths and graphs with diameter less than or equal to $2$ are dispersible.https://journals.pnu.edu.ua/index.php/cmp/article/view/1456set labeling of graphsdcsl graphsdispersible dcsl graphs |
| spellingShingle | J. Jinto K.A. Germina P. Shaini Some classes of dispersible dcsl-graphs Karpatsʹkì Matematičnì Publìkacìï set labeling of graphs dcsl graphs dispersible dcsl graphs |
| title | Some classes of dispersible dcsl-graphs |
| title_full | Some classes of dispersible dcsl-graphs |
| title_fullStr | Some classes of dispersible dcsl-graphs |
| title_full_unstemmed | Some classes of dispersible dcsl-graphs |
| title_short | Some classes of dispersible dcsl-graphs |
| title_sort | some classes of dispersible dcsl graphs |
| topic | set labeling of graphs dcsl graphs dispersible dcsl graphs |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/1456 |
| work_keys_str_mv | AT jjinto someclassesofdispersibledcslgraphs AT kagermina someclassesofdispersibledcslgraphs AT pshaini someclassesofdispersibledcslgraphs |