A Sugirtha, Y Therese Sunitha Mary
PG and Research Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai- 627002
Abstract
The semi-total point graph T₂(G) of a graph G is obtained by taking V(G) ∪ E(G) as its vertex set, where two vertices are adjacent if they are adjacent in G, or if one represents a vertex of G and the other an incident edge. In this paper, we investigate the split domination integrity SDI(G), defined asSDI(G)=min{|D|+m(G−D):D⊆V(G)},where D is a split dominating set and m(G − D) is the order of a maximum component of G − D. We derive sharp bounds and structural constraints for SDI(T₂(G)) and compute its exact values for the Cartesian product of semi-total point graphs of several families of graphs. The results generalize and extend previous work on domination parameters of semi-total point graphs by introducing the vulnerability parameter SDI to this class of graphs.
Keywords: Domination, SplitDomination, Integrity, Split Domination Integrity, Semi Total Point Graph. AMS Subject Classification: 05C38, 05C69, 05C76.
Journal Name :
EPRA International Journal of Multidisciplinary Research (IJMR)

VIEW PDF
Published on : 2025-11-02

Vol : 11
Issue : 10
Month : October
Year : 2025
Copyright © 2025 EPRA JOURNALS. All rights reserved
Developed by Peace Soft