PreprintCC BY 4.0arXiv
The Domination Reciprocal Mean Square Index
Abstract
We introduce the Domination Reciprocal Mean Square index DRMS, a new domination-degree-based topological index obtained by replacing the ordinary degree in the reciprocal mean square index with the domination degree. We establish elementary bounds in terms of graph size and extremal domination degrees, derive a one-parameter family of sharp lower bounds via the power mean, and obtain sharp bounds in terms of several well-known domination-degree-based indices, with a full characterization of the equality cases. We also compute closed-form expressions for DRMS on several standard graph families and for the corona product of two graphs.
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BibTeX
@misc{taheridehkordi2026domination,
title = {{The Domination Reciprocal Mean Square Index}},
author = {Meysam Taheri-Dehkordi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10221},
eprint = {2610.10221},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10221},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Domination Reciprocal Mean Square Index
AU - Meysam Taheri-Dehkordi
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10221
UR - https://arxiv.org/abs/2610.10221
AB - We introduce the Domination Reciprocal Mean Square index DRMS, a new domination-degree-based topological index obtained by replacing the ordinary degree in the reciprocal mean square index with the domination degree. We establish elementary bounds in terms of graph size and extremal domination degrees, derive a one-parameter family of sharp lower bounds via the power mean, and obtain sharp bounds in terms of several well-known domination-degree-based indices, with a full characterization of the equality cases. We also compute closed-form expressions for DRMS on several standard graph families and for the corona product of two graphs.
ER -