Let be a simple undirected graph. The reinforcement number of a graph is a vulnerability parameter of a graph. We have investigated a refinement that involves the average lower reinforcement number of this parameter. , denoted by , is the minimum cardinality of in that contains the edge of the complement graph . The of is defined by . In this paper, we define the average lower reinforcement number of a graph and we present the exact values for some well−known graph families.
Mots-clés : Graph vulnerability, connectivity, network design and communication, domination number, reinforcement number, average lower reinforcement number
@article{ITA_2016__50_2_135_0, author = {Turaci, Tufan and Aslan, Ersin}, title = {The average lower reinforcement number of a graph}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {135--144}, publisher = {EDP-Sciences}, volume = {50}, number = {2}, year = {2016}, doi = {10.1051/ita/2016015}, mrnumber = {3580107}, zbl = {1352.05101}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita/2016015/} }
TY - JOUR AU - Turaci, Tufan AU - Aslan, Ersin TI - The average lower reinforcement number of a graph JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2016 SP - 135 EP - 144 VL - 50 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2016015/ DO - 10.1051/ita/2016015 LA - en ID - ITA_2016__50_2_135_0 ER -
%0 Journal Article %A Turaci, Tufan %A Aslan, Ersin %T The average lower reinforcement number of a graph %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2016 %P 135-144 %V 50 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2016015/ %R 10.1051/ita/2016015 %G en %F ITA_2016__50_2_135_0
Turaci, Tufan; Aslan, Ersin. The average lower reinforcement number of a graph. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 2, pp. 135-144. doi : 10.1051/ita/2016015. http://archive.numdam.org/articles/10.1051/ita/2016015/
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