@article {
author = {Saadatmandi, Abbas and Khani, Ali and Azizi, Mohammad Reza},
title = {Numerical Calculation of Fractional Derivatives for the Sinc Functions via Legendre Polynomials},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {2},
pages = {71-86},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2018.96632.1074},
abstract = {This paper provides the fractional derivatives of the Caputo type for the sinc functions. It allows to use efficient numerical method for solving fractional differential equations. At first, some properties of the sinc functions and Legendre polynomials required for our subsequent development are given. Then we use the Legendre polynomials to approximate the fractional derivatives of sinc functions. Some numerical examples are introduced to demonstrate the reliability and effectiveness of the introduced method.},
keywords = {Sinc functions,Fractional derivatives,Collocation method,caputo derivative},
url = {http://mir.kashanu.ac.ir/article_96936.html},
eprint = {http://mir.kashanu.ac.ir/article_96936_06da74b6baa7fbe772ca4a6139f4606c.pdf}
}
@article {
author = {Hrastnik, Irena and Žerovnik, Janez},
title = {On L(d,1)-labelling of Trees},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {2},
pages = {87-102},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.227370.1211},
abstract = {Given a graph G and a positive integer d, an L(d,1)-labelling of G is a function f that assigns to each vertex of G a non-negative integer such that if two vertices u and v are adjacent, then |f(u)-f(v)|>= d and if u and v are at distance two, then |f(u)-f(v)|>= 1. The L(d,1)-number of G, λd(G), is the minimum m such that there is an L(d,1)-labelling of G with f(V)⊆ {0,1,… ,m}. A tree T is of type 1 if λd(T)= Δ +d-1 and is of type 2 if λd(T)>= Δ+d. This paper provides sufficient conditions for λd(T)=Δ+d-1 generalizing the results of Wang [11] and Zhai, Lu, and Shu [12] for L(2,1)-labelling.},
keywords = {L(d,1)-labelling,tree,Distance,Δ-vertex},
url = {http://mir.kashanu.ac.ir/article_108519.html},
eprint = {http://mir.kashanu.ac.ir/article_108519_7a815e176ecf64051ff8ea4e1a552bac.pdf}
}
@article {
author = {Kazemi, Ramin and Behtoei, Ali and Kohansal, Akram},
title = {The Zagreb Index of Bucket Recursive Trees},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {2},
pages = {103-111},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.204312.1166},
abstract = {Bucket recursive trees are an interesting and natural generalization of recursive trees. In this model the nodes are buckets that can hold up to b>= 1 labels. The (modified) Zagreb index of a graph is defined as the sum of the squares of the outdegrees of all vertices in the graph. We give the mean and variance of this index in random bucket recursive trees. Also, two limiting results on this index are given.},
keywords = {Bucket recursive tree,the Zagreb index,limiting rule},
url = {http://mir.kashanu.ac.ir/article_109509.html},
eprint = {http://mir.kashanu.ac.ir/article_109509_f3b0cb23045fab361dda93a3b444fa84.pdf}
}