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Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
Theoretical results for Perfect Location signed Roman dom...
Bojan Nikolić, Milana Grbić, Dragan Matić · 2025-01-15 · via math.CO updates on arXiv.org

The study of Roman domination has evolved to encompass a variety of challenging extensions, each contributing to the broader understanding of domination problems in graph theory. This paper explores the Perfect Location Signed Roman Domination (PLSRD) problem, a novel combination of the Perfect Roman, Locating Roman, and Signed Roman Domination paradigms. In PLSRD, each weak vertex, assigned the label -1, must be protected by exactly one strong vertex, with additional limitation that two weak vertices cannot share the same strong vertex, while the total sum of labels in the closed neighborhood of each vertex must remain positive. This paper provides exact values for the PLSRD number in several well-known graph classes, including complete graphs, complete bipartite graphs, wheels, paths, cycles, ladders, prism graphs, and 3 x n grids. Additionally, we establish a lower bound for a general 3 regular graph, as well as the upper bounds for flower snarks graphs, highlighting the intricate interplay between the PLSRD constraints and the structural properties of these graph families.