Papers by Dr. Mariam Imtiaz
Journal of Chemistry
Let ξ be a simple connected graph. The first Gourava index of graph ξ is defined as G O 1 ξ = ∑ μ... more Let ξ be a simple connected graph. The first Gourava index of graph ξ is defined as G O 1 ξ = ∑ μ η ∈ E ξ d μ + d η + d μ d η , where d μ indicates the degree of vertex μ . In this paper, we will find the upper bound of G O 1 ξ for trees of given diameter, order, size, and pendent nodes, by using some graph transformations. We will find the extremal trees and also present an ordering of these trees having this index in decreasing order.
Open Mathematics, 2020
This study focuses on finding super edge-magic total (SEMT) labeling and deficiency of imbalanced... more This study focuses on finding super edge-magic total (SEMT) labeling and deficiency of imbalanced fork and disjoint union of imbalanced fork with star, bistar and path; in addition, the SEMT strength for Imbalanced Fork is investigated.
Indonesian Journal of Combinatorics, 2020
Dutch windmill graph [1, 2] and denoted by Dnm. Order and size of Dutch windmill graph are (n−1)m... more Dutch windmill graph [1, 2] and denoted by Dnm. Order and size of Dutch windmill graph are (n−1)m+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, M-polynomials and some topological indices in term of the M-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.
Open Mathematics, 2017
It is called super edge-magic total labeling if .V .G// D f1; 2; : : : ; ng. Furthermore, if G ha... more It is called super edge-magic total labeling if .V .G// D f1; 2; : : : ; ng. Furthermore, if G has no super edge-magic total labeling, then the minimum number of vertices added to G to have a super edgemagic total labeling, called super edge-magic deficiency of a graph G, is denoted by s .G/ [4]. If such vertices do not exist, then deficiency of G will be C1. In this paper we study the super edge-magic total labeling and deficiency of forests comprising of combs, 2-sided generalized combs and bistar. The evidence provided by these facts supports the conjecture proposed by Figueroa-Centeno, Ichishima and Muntaner-Bartle [2].
Open Mathematics, 2019
A graph ℘ is said to be edge-magic total (EMT if there is a bijection Υ : V(℘) ∪ E(℘) → {1, 2, …,... more A graph ℘ is said to be edge-magic total (EMT if there is a bijection Υ : V(℘) ∪ E(℘) → {1, 2, …, |V(℘) ∪ E(℘)|} s.t., Υ(υ) + Υ(υν) + Υ(ν) is a constant for every edge υν ∈ E(℘). An EMT graph ℘ will be called strong edge-magic total (SEMT) if Υ(V(℘)) = {1, 2, …, |V(℘)|}. The SEMT strength, sm(℘), of a graph ℘ is the minimum of all magic constants a(Υ), where the minimum runs over all the SEMT valuations of ℘, this minimum is defined only if the graph has at least one such SEMT valuation. Furthermore, the SEMT deficiency of a graph ℘, μs(℘), is either the minimum non-negative integer n such that ℘ ∪ nK1 is SEMT or +∞ if there will be no such integer n. In this paper, we will present the strong edge-magicness and deficiency of disjoint union of 2-sided generalized comb with bistar, path and caterpillar, moreover we will evaluate the SEMT strength for 2-sided generalized comb.
Open Mathematics, 2018
A super edge-magic total (SEMT) labeling of a graph ℘(V, E) is a one-one map ϒ from V(℘)∪E(℘) ont... more A super edge-magic total (SEMT) labeling of a graph ℘(V, E) is a one-one map ϒ from V(℘)∪E(℘) onto {1, 2,…,|V (℘)∪E(℘) |} such that ∃ a constant “a” satisfying ϒ(υ) + ϒ(υν) + ϒ(ν) = a, for each edge υν ∈E(℘), moreover all vertices must receive the smallest labels. The super edge-magic total (SEMT) strength, sm(℘), of a graph ℘ is the minimum of all magic constants a(ϒ), where the minimum runs over all the SEMT labelings of ℘. This minimum is defined only if the graph has at least one such SEMT labeling. Furthermore, the super edge-magic total (SEMT) deficiency for a graph ℘, signified as $\mu_{s}(\wp)$ is the least non-negative integer n so that ℘∪nK1 has a SEMT labeling or +∞ if such n does not exist. In this paper, we will formulate the results on SEMT labeling and deficiency of fork, H -tree and disjoint union of fork with star, bistar and path. Moreover, we will evaluate the SEMT strength for trees.
Communications in Algebra, 2013
Let R = K[x, y, z] denote the polynomial ring in three variables over an arbitrary field K. We st... more Let R = K[x, y, z] denote the polynomial ring in three variables over an arbitrary field K. We study the factorial closure B(E) of certain R-modules E of projective dimension 1, called monomial modules. By an explicit computation, we derive an example of an algebra which is a factorial non-Cohen–Macaulay ring if the characteristic of the basic field char k is two. To this end, we study examples of monomial modules E such that the factorial closure B(E) is generated by elements of degree at most 3 over the symmetric algebra Sym(E). In order to do that it will be necessary to understand—at least partially—the third component B(E)3 of the factorial closure. This work continues the investigations of Imtiaz and Schenzel [7] were the case of monomial modules was described such that the factorial closure B(E) is generated in degrees at most two.
Open Mathematics
This study focuses on finding super edge-magic total (SEMT) labeling and deficiency of imbalanced... more This study focuses on finding super edge-magic total (SEMT) labeling and deficiency of imbalanced fork and disjoint union of imbalanced fork with star, bistar and path; in addition, the SEMT strength for Imbalanced Fork is investigated.
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Papers by Dr. Mariam Imtiaz