Results 51 to 60 of about 157 (114)
Locating‐Dominator Coloring of Some Certain Graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.Let G be a graph. A dominator coloring of G is a proper vertex coloring such that every vertex dominates all vertices of at least one color class. Given a dominator k‐coloring c with color classes Ci(1 ≤ i ≤ k) and an ordered partition Π = (C1, …, Ck) of V(G), the dominator code of a vertex v ∈ V(G) with respect to Π is defined as the k‐tuple dcΠ(v) = (
S. Nikbakht +3 more
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A Note on the Thue Chromatic Number of Lexicographic Products of Graphs
Discussiones Mathematicae Graph Theory, 2018 A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r1r2⋯r2n such that ri = rn+i for all 1 ≤ i ≤ n). Let G be a graph whose vertices are coloured.
Peterin Iztok +3 more
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On Well-Covered Direct Products
Discussiones Mathematicae Graph Theory, 2022 A graph G is well-covered if all maximal independent sets of G have the same cardinality. In 1992 Topp and Volkmann investigated the structure of well-covered graphs that have nontrivial factorizations with respect to some of the standard graph products.
Kuenzel Kirsti, Rall Douglas F.
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Extremal polyomino chains of VDB topological indices
, 2015 We show that the zig-zag chain Z3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {φij} under which the zig-zag chain Z3 n is an extremal ...
Roberto Cruz, J. Rada
semanticscholar +1 more source
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.Among the diverse types of graph products, the double join and double corona operations have remained central to many recent developments in graph theory, offering fresh insights and problem‐solving strategies. Subdivision graphs, in particular, serve as an essential tool for examining how structural modifications along edges influence the overall ...
M. Vimal +3 more
wiley +1 more source
1-Planar lexicographic products of graphs
, 2015 A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study 1-planar lexicographic products.
Jozef Bucko, J. Czap
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A New Kind of Dominated Coloring of Some Special Graphs
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper introduces the concept of locating‐dominated coloring, a new graph coloring parameter that merges the properties of dominated coloring and locating coloring. For a connected graph G, a locating‐dominated coloring is defined as a proper dominated k‐coloring of G using an ordered partition of V(G) to k‐color classes Π = (C1, C2, …, Ck) such ...
F. Poryousefi +3 more
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(Open) packing number of some graph products [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The packing number of a graph $G$ is the maximum number of closed neighborhoods of vertices in $G$ with pairwise empty intersections. Similarly, the open packing number of $G$ is the maximum number of open neighborhoods in $G$ with pairwise empty ...
Doost Ali Mojdeh +3 more
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The b-Chromatic Number of Bistar Graph
, 2014 A b-coloring is a proper vertex coloring of a graph such that each color class contains a vertex that has a neighbor in all other color classes and the b-chromatic number is the largest integer ’(G)) for which a graph has a b-coloring with ’(G) colors ...
I. T. San Diego, Frederick S. Gella
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Journal of Mathematics, Volume 2026, Issue 1, 2026.Among various graph products, the corona product continues to inspire novel research. Subdivision graphs play a key role in understanding graph behaviour under edge modifications. The estimation of Wiener index under various graph operations is of considerable importance and has attracted substantial attention in chemical graph theory.
Vimal M. +4 more
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