Results 11 to 20 of about 973,826 (351)
Domatically perfect graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 A graph of order is domatically perfect if , where and denote the domination number and the domatic number, respectively. In this paper, we give basic results for domatically perfect graphs, and study a main problem; for a given graph , to find a ...
Naoki Matsumoto
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On the perfect graph conjecture [PDF]
Discrete Mathematics, 1976 We prove the following theorem: If every, odd cycle of length ≥5 has at least two chords, then the graph is perfect.
Meyniel, H.
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Perfect Nilpotent Graphs [PDF]
Kragujevac Journal of Mathematics, 2021 Let R be a commutative ring with identity. The nilpotent graph of R, denoted by ΓN(R), is a graph with vertex set ZN(R)∗, and two vertices x and y are adjacent if and only if xy is nilpotent, where ZN(R) = {x ∈ R∣xy is nilpotent, for some y ∈ R∗}. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the ...
Nikmehr, M. J., Azadi, A.
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Journal of Combinatorial Theory, Series B, 2018 Let $G=(V,E)$ be a graph and let $A_G$ be the clique-vertex incidence matrix of $G$. It is well known that $G$ is perfect iff the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$ is totally dual integral (TDI). In 1982, Cameron and Edmonds proposed to call $G$ box-perfect if the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$
Guoli Ding, Wenan Zang, Qiulan Zhao
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Discrete Applied Mathematics, 2019 Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph $G$ to be sum-perfect if for every induced subgraph $H$ of $G$, $α(H) + ω(H) \geq |V(H)|$. (Here $α$ and $ω$ denote the stability number and clique number, respectively.) We give a set of $27$ graphs and we prove that a graph $G$ is sum-perfect if and only if $G ...
Bart Litjens +2 more
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Perfectness of clustered graphs [PDF]
Discrete Optimization, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flavia Bonomo +3 more
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Triple Connected Domination Number of a Graph [PDF]
, 2012 The concept of triple connected graphs with real life application was introduced by considering the existence of a path containing any three vertices of a graph G.
Selvam Avadayappan +7 more
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Latent Diffusion Process With Mechanistic Guidance For Designing Functionally Graded Metamaterials With Perfect Connectivity. [PDF]
Adv Sci (Weinh)A latent diffusion‐based framework is proposed for designing functionally graded metamaterials with perfect connectivity. By integrating vector‐quantized latent representations with mechanistic guidance, the framework enables accurate inverse design toward target elastic properties.
Yu J, Lee D, Kim N.
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Extremal Values of Variable Sum Exdeg Index for Conjugated Bicyclic Graphs
Journal of Chemistry, 2021 A connected graph GV,E in which the number of edges is one more than its number of vertices is called a bicyclic graph. A perfect matching of a graph is a matching in which every vertex of the graph is incident to exactly one edge of the matching set ...
Muhammad Rizwan +3 more
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Random Structures & Algorithms, 2018 We investigate the asymptotic structure of a random perfect graph Pn sampled uniformly from the set of perfect graphs on vertex set . Our approach is based on the result of Prömel and Steger that almost all perfect graphs are generalised split graphs, together with a method to generate such graphs almost uniformly.
McDiarmid, C, Yolov, N
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