Compatibility property of steady systems

1968 ◽  
Vol 14 (5) ◽  
pp. 429-432 ◽  
Author(s):  
A. A. Filyukov
Keyword(s):  
Compatibility Property

ON THE PAIRWISE COMPATIBILITY PROPERTY OF SOME SUPERCLASSES OF THRESHOLD GRAPHS

2013 ◽  
Vol 05 (02) ◽  
pp. 1360002 ◽  
Author(s):  
TIZIANA CALAMONERI ◽  
ROSSELLA PETRESCHI ◽  
BLERINA SINAIMERI
Keyword(s):  
The Other ◽  
Real Numbers ◽  
Weighted Tree ◽  
Positive Edge ◽  
Threshold Graphs ◽  
Compatibility Graph ◽  
Unique Path ◽  
Compatibility Property

A graph G is called a pairwise compatibility graph (PCG) if there exists a positive edge weighted tree T and two non-negative real numbers d min and d max such that each leaf lu of T corresponds to a node u ∈ V and there is an edge (u, v) ∈ E if and only if d min ≤ dT (lu, lv) ≤ d max , where dT (lu, lv) is the sum of the weights of the edges on the unique path from lu to lv in T. In this paper we study the relations between the pairwise compatibility property and superclasses of threshold graphs, i.e., graphs where the neighborhoods of any couple of nodes either coincide or are included one into the other. Namely, we prove that some of these superclasses belong to the PCG class. Moreover, we tackle the problem of characterizing the class of graphs that are PCGs of a star, deducing that also these graphs are a generalization of threshold graphs.

scholarly journals Fixed point results for Suzuki Type Σ-contractions via simulation functions in modular b-metric spaces

2020 ◽  
Author(s):  
Mahpeyker ÖZTÜRK ◽  
Abdurrahman Buyukkaya
Keyword(s):  
Fixed Point ◽  
Graph Theory ◽  
Common Fixed Point ◽  
Homotopy Theory ◽  
Metric Spaces ◽  
Simulation Functions ◽  
Compatibility Property

This study aims to introduce Suzuki type Σcontraction mappings with simulation functions in the frame of modular b-metric spaces. Also, some coincidence and common fixed point results are obtained for four mappings using the weakly compatibility property that these results are the extensions and improvements of the existing literature. Finally, we also present two applications on graph theory and homotopy theory, which show applicability and validity of our results.

scholarly journals A general common fixed point theorem of Meir and Keeler type for noncontinuous weak compatible mappings

Filomat ◽  
2004 ◽  
pp. 33-40 ◽  
Author(s):  
Valeriu Popa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Compatible Mappings ◽  
Implicit Relation ◽  
Weak Compatibility ◽  
Combination Of Methods ◽  
Common Fixed Point Theorem ◽  
Compatibility Property

In this paper, using a combination of methods used in [1],[20] and [22] the results from [3, Theorem 1], [14,Theorem 1] and [15, Theorem 1] are improved by removing the assumption of continuity, relaxing compatibility to weak compatibility property and replacing the completeness of the space with a set of four alternative conditions for functions satisfying an implicit relation.

Good subsemigroups of ℕn

2018 ◽  
Vol 28 (02) ◽  
pp. 179-206 ◽  
Author(s):  
Marco D’Anna ◽  
Pedro A. García-Sánchez ◽  
Vincenzo Micale ◽  
Laura Tozzo
Keyword(s):  
Algebraic Curve ◽  
Algebraic Curves ◽  
Good System ◽  
Canonical Ideal ◽  
Compatibility Property ◽  
Algebraic Counterpart

Value semigroups of non-irreducible singular algebraic curves and their fractional ideals are submonoids of [Formula: see text] that are closed under infimums, have a conductor and fulfill a special compatibility property on their elements. Monoids of [Formula: see text] fulfilling these three conditions are known in the literature as good semigroups and there are examples of good semigroups that are not realizable as the value semigroup of an algebraic curve. In this paper, we consider good semigroups independently from their algebraic counterpart, in a purely combinatorial setting. We define the concept of good system of generators, and we show that minimal good systems of generators are unique. Moreover, we give a constructive way to compute the canonical ideal and the Arf closure of a good subsemigroup when [Formula: see text].

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