Geodesic
Metric dimension and zero forcing number of two families of line graphs
Mathematica Bohemica, Tome 139 (2014) no. 3, pp. 467-483.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the “AIM Minimum Rank–Special Graphs Work Group”, whereas metric dimension is a well-known graph parameter. We investigate the metric dimension and the zero forcing number of some line graphs by first determining the metric dimension and the zero forcing number of the line graphs of wheel graphs and the bouquet of circles. We prove that $Z(G) \le 2Z(L(G))$ for a simple and connected graph $G$. Further, we show that $Z(G) \le Z(L(G))$ when $G$ is a tree or when $G$ contains a Hamiltonian path and has a certain number of edges. We compare the metric dimension with the zero forcing number of a line graph by demonstrating a couple of inequalities between the two parameters. We end by stating some open problems.
DOI : 10.21136/MB.2014.143937
Classification : 05C05, 05C12, 05C38, 05C50
Keywords: resolving set; metric dimension; zero forcing set; zero forcing number; line graph; wheel graph; bouquet of circles 
@article{10_21136_MB_2014_143937,
     author = {Eroh, Linda and Kang, Cong X. and Yi, Eunjeong},
     title = {Metric dimension and zero forcing number of two families of line graphs},
     journal = {Mathematica Bohemica},
     pages = {467--483},
     publisher = {mathdoc},
     volume = {139},
     number = {3},
     year = {2014},
     doi = {10.21136/MB.2014.143937},
     mrnumber = {3269369},
     zbl = {06391466},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.143937/}
}
TY  - JOUR
AU  - Eroh, Linda
AU  - Kang, Cong X.
AU  - Yi, Eunjeong
TI  - Metric dimension and zero forcing number of two families of line graphs
JO  - Mathematica Bohemica
PY  - 2014
SP  - 467
EP  - 483
VL  - 139
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.143937/
DO  - 10.21136/MB.2014.143937
LA  - en
ID  - 10_21136_MB_2014_143937
ER  - 
%0 Journal Article
%A Eroh, Linda
%A Kang, Cong X.
%A Yi, Eunjeong
%T Metric dimension and zero forcing number of two families of line graphs
%J Mathematica Bohemica
%D 2014
%P 467-483
%V 139
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.143937/
%R 10.21136/MB.2014.143937
%G en
%F 10_21136_MB_2014_143937
Eroh, Linda; Kang, Cong X.; Yi, Eunjeong. Metric dimension and zero forcing number of two families of line graphs. Mathematica Bohemica, Tome 139 (2014) no. 3, pp. 467-483. doi : 10.21136/MB.2014.143937. http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.143937/

Cité par Sources :