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Trees with Distinguishing Index Equal Distinguishing Number Plus One

Discussiones Mathematicae Graph Theory, 2020
The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism.
Alikhani Saeid, Klavžar Sandi, Lehner Florian, Soltani Samaneh   +3 more
doaj   +1 more source

The Neighbor-Locating-Chromatic Number of Pseudotrees

, 2020
A $k$-coloring of a graph $G$ is a partition of the set of vertices of $G$ into $k$ independent sets, which are called colors. A $k$-coloring is neighbor-locating if any two vertices belonging to the same color can be distinguished from each other by the
Alcon, Liliana, Gutierrez, Marisa, Hernando, Carmen, Mora, Mercè, Pelayo, Ignacio M.   +4 more
core  

Restrained domination in unicyclic graphs

Discussiones Mathematicae Graph Theory, 2009
Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γr(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle.
Johannes H. Hattingh, Ernst J. Joubert, Marc Loizeaux, Andrew R. Plummer, Lucas C. van der Merwe   +4 more
openaire   +1 more source

The Least Algebraic Connectivity of Graphs

Discrete Dynamics in Nature and Society, 2015
The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected.
Guisheng Jiang, Guidong Yu, Jinde Cao
doaj   +1 more source

Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination

IEEE Access, 2019
Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M1 and the second Zagreb index M2 have already studied. In particular, it has been presented, the first Zagreb index M1 and the second Zagreb index M2 of trees T in ...
Doost Ali Mojdeh, Mohammad Habibi, Leila Badakhshian, Yongsheng Rao   +3 more
doaj   +1 more source

A STUDY ON UNICYCLIC GRAPH

, 2020
{"references": ["1.\tJ. Amalorpava Jerline, L. Benedict Michaelraj, On a conjecture of harmonic index and diameter of graphs, Kragujevac Journal of Mathematics, 40(1), (2016),73-78. 2.\tR. Balakrishnan, K. Ranganathan, A Textbook of Graph Theory, Springer-Verlog, New York, 2000. 3.\tH. Deng, S. Balachandran, S. K. Ayyaswamy, Y. B.
I. Ignomary, S. Suganya
openaire   +1 more source

Isolate Domination in Unicyclic Graphs

International Journal of Mathematics and Soft Computing, 2013
A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called a dominating set of $G$ if every vertex in $V-D$ is adjacent to a vertex in $D$. A dominating set $D$ such that $$ has an isolated vertex is called an isolate dominating set and the minimum cardinality of an isolate dominating set is called the isolate domination number of $G$ and is ...
S. Balamurugan, I. Sahul Hamid
openaire   +1 more source

Solutions of Detour Distance Graph Equations. [PDF]

Sensors (Basel), 2022
Prabha SC, Palanivel M, Amutha S, Anbazhagan N, Cho W, Song HK, Joshi GP, Moon H.   +7 more
europepmc   +1 more source

Eigenspaces for \(-2\) in signed line graphs

The American Journal of Combinatorics
It is known that \(-2\) appears in the spectrum of a connected signed line graph if and only if its root is either (a) a balanced signed graph, not a tree, that spans a switching of the complete signed graph or (b) an unbalanced simply signed graph ...
Zoran Stanić
doaj   +1 more source

A structural approach to the graceful coloring of a subclass of trees. [PDF]

Heliyon, 2023
D L, S DY.
europepmc   +1 more source