dc.contributor.author |
Ciftci, C. |
|
dc.contributor.author |
Aytac, A. |
|
dc.date.accessioned |
2023-01-06T11:35:04Z |
|
dc.date.available |
2023-01-06T11:35:04Z |
|
dc.date.issued |
2021 |
|
dc.identifier.citation |
Ciftci, C., Aytac, A. (2021). A Vulnerability Parameter of Networks. Mathematical Notes, 109, 517-526.Doi:10.1134/S0001434621030202 |
en_US |
dc.identifier.isbn |
0001-4346 |
|
dc.identifier.isbn |
1573-8876 |
|
dc.identifier.uri |
http://dx.doi.org/10.1134/S0001434621030202 |
|
dc.identifier.uri |
https://www.webofscience.com/wos/woscc/full-record/WOS:000670513100020 |
|
dc.identifier.uri |
http://earsiv.odu.edu.tr:8080/xmlui/handle/11489/3530 |
|
dc.description |
WoS Categories : Mathematics
Web of Science Index : Science Citation Index Expanded (SCI-EXPANDED)
Research Areas : Mathematics |
en_US |
dc.description.abstract |
The vulnerability in a communication network is the measurement of the strength of the network against damage that occurs in nodes or communication links. It is important that a communication network is still effective even when it loses some of its nodes or links. In other words, since a network can be modelled by a graph, it is desired to know whether the graph is still connected when some of the vertices or edges are removed from a connected graph. The vulnerability parameters aim to find the nature of the network when a subset of the nodes or links is removed. One of these parameters is domination. Domination is a measure of the connection of a subset of vertices with its complement. In this paper, we study porous exponential domination as a vulnerability parameter and obtain certain results on the Cartesian product and lexicographic product graphs. We determine the porous exponential domination number, denoted by. gamma*(e), of the Cartesian product of P-2 with P-n and C-n, separately. We also determine the porous exponential domination number of the Cartesian product of P-n with complete bipartite graphs and any graph G which has a vertex of degree vertical bar V(G)vertical bar - 1. Moreover, we obtain the porous exponential domination number of the lexicographic product of P-n and G(m), denoted by P-n[G(m)], for the case where G(m) is a graph of order m with a vertex of degree m - 1 and for the opposite case where G(m) is a graph of order m which has no vertex of degree m - 1. We further show that gamma*(e)(P-n[G(m)]) = gamma*(e)(G(m)[P-n]) = gamma*(e)(P-n) by proving gamma*(e)(G(m)[G(n)]) = gamma*(e)(G(n)), where G(m) is a graph of order m with a vertex of degree m - 1 and G(n) is any graph of order n. |
en_US |
dc.language.iso |
eng |
en_US |
dc.publisher |
MAIK NAUKA/INTERPERIODICA/SPRINGER NEW YORK |
en_US |
dc.relation.isversionof |
10.1134/S0001434621030202 |
en_US |
dc.rights |
info:eu-repo/semantics/openAccess |
en_US |
dc.subject |
EXPONENTIAL DOMINATION |
en_US |
dc.subject |
network design and communication; graph vulnerability; domination; exponential domination; porous exponential domination; Cartesian product; lexicographic product |
en_US |
dc.title |
A Vulnerability Parameter of Networks |
en_US |
dc.type |
article |
en_US |
dc.relation.journal |
MATHEMATICAL NOTES |
en_US |
dc.contributor.department |
Ordu Üniversitesi |
en_US |
dc.identifier.volume |
109 |
en_US |
dc.identifier.startpage |
517 |
en_US |
dc.identifier.endpage |
526 |
en_US |