Product of interval-valued fuzzy graphs and degree

Rashmanlou, Hossein; Pal, Madhumangal; Borzooei, Rajab Ali; Mofidnakhaei, Farshid; Sarkar, Biswajit

doi:10.3233/jifs-181488

Cited by 34 publications

(33 citation statements)

References 19 publications

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“…Sahoo and Pal [22] presented some operations on intuitionistic fuzzy graph (IFG) products and calculated the vertex degree in the IFGs. Rashmanlou et al [23] proposed product operations over a range of values fuzzy graphs, that is, interval-valued fuzzy graphs and discussed the degree of a vertex in fuzzy graphs with interval values. Recently, Naz et al [15] studied some of the PFG operations, the vertex degree and the vertex total degree in the PFG.…”

Section: Introductionmentioning

confidence: 99%

Maximal Product of Graphs under Vague Environment

Hoseini

Akram

Hosseini

et al. 2020

MCA

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Graph models are found everywhere in natural and human made structures, including process dynamics in physical, biological and social systems. The product of graphs are appropriately used in several combinatorial applications and in the formation of different structural models. In this paper, we present a new product of graphs, namely, maximal product of two vague graphs. Then we describe certain concepts, including strongly, completely, regularity and connectedness on a maximal product of vague graphs. Further, we consider some results of edge regular and totally edge regular in a maximal product of vague graphs. Finally, we present an application for optimization of the biomass based on a maximal product of vague graphs.

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Section: Introductionmentioning

confidence: 99%

Maximal Product of Graphs under Vague Environment

Hoseini

Akram

Hosseini

et al. 2020

MCA

Self Cite

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“…Sahoo and Pal [34] presented some product operations on IFGs and calculated the degree of a vertex in IFGs. Rashmanlou et al [35] proposed product operations on interval-valued fuzzy graphs and study about the degree of a vertex in interval-valued fuzzy graphs. Naz et al [21] discussed some product operations of SVNGs and applied SVNGs to multi-criteria decision-making.…”

Section: Introductionmentioning

confidence: 99%

Product Operations on q-Rung Orthopair Fuzzy Graphs

Yin

Yang

2019

Symmetry

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The q-rung orthopair fuzzy graph is an extension of intuitionistic fuzzy graph and Pythagorean fuzzy graph. In this paper, the degree and total degree of a vertex in q-rung orthopair fuzzy graphs are firstly defined. Then, some product operations on q-rung orthopair fuzzy graphs, including direct product, Cartesian product, semi-strong product, strong product, and lexicographic product, are defined. Furthermore, some theorems about the degree and total degree under these product operations are put forward and elaborated with several examples. In particular, these theorems improve the similar results in single-valued neutrosophic graphs and Pythagorean fuzzy graphs.

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“…Ramya and Lavanya (2017) studied the edge contraction on bipolar fuzzy graphs (Massa'deh and Ba'arah, 2013) introduced the concept of degrees types in bipolar fuzzy graphs. Akram and Dudek (2011) extended the fuzzy set theory to interval-valued fuzzy sets, in addition (Ramprasad et al, 2016) discussed interval valued fuzzy graphs, also (Massa'deh, 2017) discussed regular, degree of vertex, strong, complete interval valued fuzzy graphs (Rashmanlou and Pal, 2013a-c;Rashmanlou and Jun, 2013). Mishra et al studied bipolar interval valued fuzzy graphs (Mishra and Pal, 2016).…”

Section: Introductionmentioning

confidence: 99%