摘要 :
Fuzzy graph theory provides tools for modeling different types of real-world networks. However, we should consider more relations, especially the relationship between edges with their corresponding vertices, which usually refer to...
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Fuzzy graph theory provides tools for modeling different types of real-world networks. However, we should consider more relations, especially the relationship between edges with their corresponding vertices, which usually refer to incidences, when external factors influence the real flow in a network. Then, fuzzy incidence graphs may sometimes model certain real-world situations better. The present study aims to define incidence valid edges, the recognition of which is easy, and their number is more than that of effective edges. In this regard, we introduce dominating sets in fuzzy incidence graphs by using incidence valid edges due to the importance of the concept of domination and its application in various issues. In addition, several important sets related to the dominating set such as independent and irredundant sets are investigated. Further, the concepts of domination, upper domination, and independent domination number, as well as independence, irredundant, and upper irredundant number in fuzzy incidence graphs are evaluated, along with their relation. Finally, an application of the concept of domination in a fuzzy incidence graph is obtained.
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The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey. They conjectured that every graph G can be incidence colored with Δ(G)+2 colors. In this paper, the trueness of this conjecture for co...
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The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey. They conjectured that every graph G can be incidence colored with Δ(G)+2 colors. In this paper, the trueness of this conjecture for complete k-partite graph was proved, and the incidence chromatic number of complete k-partite graphs was calculated.
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The notion of a fuzzy end node in fuzzy incidence graphs is developed in this article. The concept of a fuzzy incidence graph is new and should be very useful in applications in fuzzy graphs and fuzzy networks. Relationships betwe...
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The notion of a fuzzy end node in fuzzy incidence graphs is developed in this article. The concept of a fuzzy incidence graph is new and should be very useful in applications in fuzzy graphs and fuzzy networks. Relationships between weak incidence pairs and fuzzy incidence end nodes and fuzzy incidence cut vertices are developed.
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Brualdi and Massey in 1993 posed two conjectures regarding the upper bound for incidence coloring number of graphs in terms of maximum degree. In this paper among some results, we prove these conjectures for some classes of graphs...
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Brualdi and Massey in 1993 posed two conjectures regarding the upper bound for incidence coloring number of graphs in terms of maximum degree. In this paper among some results, we prove these conjectures for some classes of graphs with maximum degree 4.
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We show that if the number I of incidences between m points and n planes in R~3 is sufficiently large, then the incidence graph (which connects points to their incident planes) contains a large complete bipartite subgraph involvin...
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We show that if the number I of incidences between m points and n planes in R~3 is sufficiently large, then the incidence graph (which connects points to their incident planes) contains a large complete bipartite subgraph involving r points and s planes, so that rs ≥ I~2/mn - a(m + n), for some constant a > 0. This is shown to be almost tight in the worst case because there are examples of arbitrarily large sets of points and planes where the largest complete bipartite incidence subgraph records only I~2/mn - m+n/16 incidences. We also take some steps towards generalizing this result to higher dimensions.
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Incidence blocks in fuzzy incidence graphs (FIGs) are studied in this paper. Incidence relations play very important roles in several natural and human made networks like road, pipe, power and data flow networks. Incidence blocks ...
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Incidence blocks in fuzzy incidence graphs (FIGs) are studied in this paper. Incidence relations play very important roles in several natural and human made networks like road, pipe, power and data flow networks. Incidence blocks are characterized using strongest strong incidence paths. A more concrete structure called cyclically strong FIG (CSFIG) is also introduced and an application of fuzzy incidence blocks in illegal international migration is proposed.
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The similarity incidence degree has been proved to be an ideal model, which satisfies both uniform and parallel properties. The special incidence degree that is both closeness and similarity is found non-existent, but there exists...
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The similarity incidence degree has been proved to be an ideal model, which satisfies both uniform and parallel properties. The special incidence degree that is both closeness and similarity is found non-existent, but there exists neither closeness nor similarity incidence degree. And the method of similarity incidence degree derived from closeness incidence degree was put forward It. illustrates the widespread existence of closeness incidence degree and similarity incidence degree by constructing a new closeness incidence degree and deriving the corresponding similarity incidence degree.
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In this paper, the model of Chattopadhyay and Bairagi1 has been modified by considering the horizontal incidence as standard incidence in lieu of mass action incidence. Our observations indicate that the modified system around the...
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In this paper, the model of Chattopadhyay and Bairagi1 has been modified by considering the horizontal incidence as standard incidence in lieu of mass action incidence. Our observations indicate that the modified system around the positive equilibrium is stable for a wider range of force of infection. Numerical experiments are performed to observe the effect of disease transmission on different types of functional responses. We finally conclude that the mechanistic nature of disease transmission should be known for predicting the dynamics of such systems.
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In this paper we measure the Fuzzy incidence chromatic numbers of certain Fuzzy incidence graphs. We apply Fuzzy incidence coloring to real-world problems to monitor human loss during accidents by adhering to traffic flow laws and...
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In this paper we measure the Fuzzy incidence chromatic numbers of certain Fuzzy incidence graphs. We apply Fuzzy incidence coloring to real-world problems to monitor human loss during accidents by adhering to traffic flow laws and in particular, reducing traffic flow waiting times.
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