Results 11 to 20 of about 1,716,586 (315)
Perfect codes in Cayley sum graphs [PDF]
Electronic Journal of Combinatorics, 2020 A subset $C$ of the vertex set of a graph $\Gamma$ is called a perfect code of $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to exactly one vertex in $C$. Let $A$ be a finite abelian group and $T$ a square-free subset of $A$.
Xuanlong Ma, Kaishun Wang, Yuefeng Yang
openalex +3 more sources
A new characterization of trivially perfect graphs
Electronic Journal of Graph Theory and Applications, 2015 A graph $G$ is \emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number) $\alpha(G)$ equals the number of (maximal) cliques $m(G)$.
Christian Rubio Montiel
doaj +2 more sources
Nearly perfect sets in products of graphs [PDF]
Opuscula Mathematica, 2004 The study of nearly perfect sets in graphs was initiated in [Dunbar J. E., Harris F. C., Hedetniemi S. M., Hedetniemi S. T., McRae A. A., Laskar R. C.: Nearly perfect sets in graphs. Discrete Mathematics 138 (1995), 229-246]. Let \(S\subseteq V(G)\).
Maria Kwaśnik, Monika Perl
doaj +1 more source
Submodular Functions and Perfect Graphs [PDF]
Mathematics of Operations Research, 2021 We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph.
Tara Abrishami +3 more
semanticscholar +1 more source
The spanning k-trees, perfect matchings and spectral radius of graphs [PDF]
Linear and multilinear algebra, 2021 A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we provide a sufficient condition for the existence of a k-tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless ...
Dandan Fan +3 more
semanticscholar +1 more source
Strong Perfect Cobondage Number of Standard Graphs
Ratio Mathematica, 2023 Let G be a simple graph. A subset S Í V(G) is called a strong (weak) perfect dominating set of G if |Ns(u) ∩ S| = 1(|Nw(u) ∩ S| = 1) for every u ∊V(G) - S where Ns(u) = {v ∊ V(G) / uv deg v ≥ deg u} (Nw(u) = {v ∊V(G) / uv deg v ≤ deg u}.
T. S Govindalakshmi, N Meena
doaj +1 more source
Padmakar-Ivan Index of Some Types of Perfect Graphs
Discrete Mathematics Letters, 2022 The Padmakar-Ivan (PI) index of a graph G is defined as PI ( G ) = (cid:80) e ∈ E ( G ) ( | V ( G ) | − N G ( e )) , where N G ( e ) is the number of equidistant vertices for the edge e . A graph is perfect if for every induced subgraph H , the equation χ
Manju Sankaramalil Chithrabhanu +1 more
semanticscholar +1 more source
Perfect double Italian domination of a graph
AKCE International Journal of Graphs and Combinatorics, 2023 For a graph [Formula: see text] with [Formula: see text] and [Formula: see text], a perfect double Italian dominating function is a function [Formula: see text] having the property that [Formula: see text], for every vertex [Formula: see text] with ...
Guoliang Hao +2 more
doaj +1 more source
The Chromatic Symmetric Functions of Trivially Perfect Graphs and Cographs [PDF]
Graphs and Combinatorics, 2017 Richard P. Stanley defined the chromatic symmetric function of a simple graph and has conjectured that every tree is determined by its chromatic symmetric function.
Shuhei Tsujie
semanticscholar +1 more source
Perfect Fuzzy Soft Tripartite Graphs and Their Complements
Discrete Dynamics in Nature and Society, 2022 Fuzzy soft graphs are efficient numerical tools for simulating the uncertainty of the real world. A fuzzy soft graph is a perfect fusion of the fuzzy soft set and the graph model that is widely used in a variety of fields.
Kalaichelvan Kalaiarasi +4 more
doaj +1 more source