TY  - JOUR
T1  - Transversal Semitotal Domination Number in Graphs
AU  - Kartal Yıldız, Zeliha
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.53570/jnt.1720611
JF  - Journal of New Theory
JO  - JNT
PB  - Naim ÇAĞMAN
WT  - DergiPark
SN  - 2149-1402
SP  - 1
EP  - 8
IS  - 52
LA  - en
AB  - A transversal semitotal dominating set in a graph $G$ is a subset of vertices that intersects every minimal semitotal dominating set of \( G \) and itself forms a semitotal dominating set. Among all sets that intersect each semitotal dominating set of a graph \( G \), the one with the smallest cardinality defines a key parameter in the present study. This parameter is referred to as the transversal semitotal domination number and is denoted by \( \gamma_{tt2}(G) \). This paper investigates fundamental properties of this parameter in arbitrary graphs and determines exact values of \( \gamma_{tt2}(G) \) for several standard graph classes, including complete, star, wheel, cycle, path, and complete bipartite graphs.
KW  - Graph theory
KW  - domination
KW  - semitotal domination
KW  - transversal semitotal domination
CR  - G. Chartrand, L. Lesniak, Graphs and digraphs, Chapman and Hall, 1996.
CR  - C. A. Barefoot, R. Entringer, H. Swart, Vulnerability in graphs: a comparative survey, Journal of Combinatorial Mathematics and Combinatorial Computing 1 (1987) 13--22.
CR  - Ö. K. Kürkçü, E. Aslan, A comparison between edge neighbor rupture degree and edge scattering number in graphs, International Journal of Foundations of Computer Science 29 (07) (2018) 1119--1142.
CR  - E. Aslan, Ö. K. Kürkçü, Edge scattering number of gear graphs, Bulletin of The International Mathematical Virtual Institute 5 (1) (2015) 25--31.
CR  - T. W. Haynes, S. T. Hedetniemi, P. J. Slater, Fundamentals of domination in graphs, CRC Press, 1998.
CR  - E. J. Cockayne, R. W. Dawes, S. T. Hedetniemi, Total domination in graphs, Networks 10 (3) (1980) 211--219.
CR  - W. Goddard, M. A. Henning, C. A. McPillan, Semitotal domination in graphs, Utilitas Mathematica 94 (2014) 67--81.
CR  - T. W. Haynes, M. A. Henning, Trees with unique minimum semitotal dominating sets, Graphs and Combinatorics 36 (2020) 689--702.
CR  - Z. Kartal, A. Aytaç, Semitotal domination of Harary graphs, Tbilisi Mathematical Journal 13 (3) (2020) 11--17.
CR  - Z. Kartal Yıldız, A. Aytaç, Semitotal domination of some known trees, Bulletin of the International Mathematical Virtual Institute 11 (1) (2021) 147--158.
CR  - B. L. Susada, R. G. Eballe, Independent semitotal domination in the join of graphs, Asian Research Journal of Mathematics 19 (3) (2023) 25--31.
CR  - B. L. Susada, R. G. Eballe, Independent semitotal domination in the corona of graphs, Advances and Applications in Discrete Mathematics 39 (1) (2024) 89--98.
CR  - N. Alon, M. R. Fellows, D. R. Hare, Vertex transversals that dominate, Journal of Graph Theory 21 (1) (1996) 21--31.
CR  - M. R. Fellows, Transversals of vertex partitions in graphs, SIAM Journal on Discrete Mathematics 3 (2) (1990) 206--215.
CR  - I. S. Hamid, Independent transversal domination in graphs, Discussiones Mathematicae Graph Theory 32 (1) (2012) 5--17.
CR  - A. Aytaç, C. Erkal, Independent transversal domination number in complementary prisms, Honam Mathematical Journal 43 (1) (2021) 17--25.
CR  - H. A. Ahangar, V. Samodivkin, I. G. Yero, Independent transversal dominating sets in graphs: Complexity and structural properties, Filomat 30 (2) (2016) 293--303.
CR  - N. M. G. Cotejo, E. D. Benacer, On neighbourhood transversal domination of some graphs, Advances and Applications in Discrete Mathematics 28 (2) (2021) 205--215.
CR  - A. C. Mart\'{ı}nez, I. Peterin, I. G. Yero, Independent transversal total domination versus total domination in trees, Discussiones Mathematicae Graph Theory 41 (1) (2021) 213--224.
CR  - M. A. O. Bonsocan, F. P. Jamil, Transversal hop domination in graphs, European Journal of Pure and Applied Mathematics 16 (1) (2023) 192--206.
CR  - M. A. O. Bonsocan, F. P. Jamil, Transversal total hop domination in graphs, Discrete Mathematics, Algorithms and Applications 16 (7) (2024) 2350095.
CR  - Z. Kartal Yıldız, A. Aytaç, Semitotal domination number of some graph operations, Numerical Methods for Partial Differential Equations 39 (3) (2023) 1841--1850.
CR  - S. R. Nayaka, A. Alwardi, Puttaswamy, Transversal domination in graphs, Gulf Journal of Mathematics 6 (2) (2018) 41--49.
UR  - https://doi.org/10.53570/jnt.1720611
L1  - https://dergipark.org.tr/en/download/article-file/4963360
ER  -