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Latest Issue

Volume 13, No. 2, June 2020




Chinmayi Indices of some Graph Operations

In this paper, we investigate the mathematical properties of a set of new novel topological indices named as Chinmayi indices. We obtain closed formulae for Chinmayi indices of some class of graphs. Further, we obtain first Chinmayi index of some graph operations viz., Cartesian product, composition, tensor product, and corona product of two graphs. Lastly, as an application of graph operations, we derive explicit formulae for some chemically important structures and nano materials.


B. Basavanagoud
Anand P. Barangi



JJMS, 2020, 13(2), 169-187


In this paper, the notion of subdifferential is extended in the framework of abstract convexity and some basic properties of this new concept is considered.
Also, a representation based on maximal elements is given. Our results is supported by some examples.


Zakieh Farabi
Mohsen Alimohammady
Mehdi Roohi


JJMS, 2020, 13(2), 189-202


Generalized Complex Space Forms

In this paper, we find an eigen value of Ricci operator corresponding to scalar curvature r of a generalized complex space form and we give conditions for the existence of a generalized complex space form.


Uppara Manjulamma
Nagaraja H. G.
Kiran Kumar D. L.


JJMS, 2020, 13(2), 203-219

3-Divisor Cordial Labeling of some Join Graphs

Let G be a (p, q) graph and 2 ≤ k ≤ p. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label 1 if either f(u) or f(v) divides the other and 0 otherwise. f is called a k-divisor cordial labeling

if |vf (i) − vf (j)| ≤ 1, i, j ϵ {1, 2, ..., k} and |ef (0) − ef (1)| ≤ 1 where

vf (x) denotes the number of vertices labeled with x, where x ϵ {1, 2, . . . , k}, ef (i) denote the number of edges labeled with i, i ϵ {0, 1}. A graph with a k-divisor cordial labeling is called a k-divisor cordial graph. In this paper, we discuss 3-divisor cordial labeling behavior of wheel and Kn + 2K2.  



S. Sathish Narayanan


JJMS, 2020, 13(2), 221-230


Complex Fuzzy Lie Algebras

A complex fuzzy Lie algebra is a fuzzy Lie algebra whose membership function takes values in the unit circle in the complex plane. In this paper, we define the complex fuzzy Lie subalgebras and complex fuzzy ideals of Lie algebras.
Then, we investigate some of characteristics of complex fuzzy Lie subalgebras. The relationship between complex fuzzy Lie subalgebras and fuzzy Lie subalgebrasis also investigated. Finally, we define the image and the inverse image of complex fuzzy Lie subalgebra under Lie algebra homomorphism. The properties of complex fuzzy Lie subalgebras and complex fuzzy ideals under homomorphisms of Lie algebras are studied.


Shadi Shaqaqha



JJMS, 2020, 13(2), 231-247


Compatible and Weakly Compatible Maps in a Complex Fuzzy Metric Space

In this paper we introduce the notion of compatibility of self maps in a complex fuzzy metric space. Using this, we establish some common fixed point theorems employing a generalized contractive condition, which extend and generalize the existing results in fuzzy metric spaces to a complex fuzzy metric space. They also generalize the existing results of Singh et al.[13] in a complex fuzzy metric space.


Shobha Jain
Shishir Jain



JJMS, 2020, 13(2), 249-267


Cost Analysis of Degraded Machining System with Spare, Common Cause Failure and Operating under Variable Service Rate

In this Paper, we have studied the machining system with finite number of operating machines along with warm standby machines under the supervision of R heterogeneous repairmen. The repairmen are servicing with variable service rate. Whenever any machine fails, it is immediately replaced by available standby machine. Machine may also fail due to common cause. Once all the standbys are exhausted, the system has extra burden to share load of failures and it starts to work under degraded mode. It is assumed that, the time-to-failure and time-to-service of the machines follows the exponential distribution. Steady state probability is evaluated using recursive algorithm. We have developed a cost model to obtain the optimum number of repairmen and standbys maintaining the system availability at minimum specified level. Under optimum operating conditions, various system performance measures are evaluated and sensitivity analysis is also performed.



Praveen Deora
Dinesh Chandra Sharma
Purushottam Jharotia



JJMS, 2020, 13(2), 269-285



Transmuted Aradhana Distribution: Properties and Application

In this paper, we introduce a new continuous distribution called transmuted Aradhana distribution (TAD). It is a generalization of Aradhana distribution based on the quadratic rank transmutation map. Properties of the proposed distribution including shape of the density, reliability and hazard rate functions, mean residual life function, r th moment, moment generating function, order statistics, Renyi entropy, quantile function, are explored. We use maximum likelihood method and method of moments to estimate the parameters of the TAD. We present an application to real life data set to illustrate the usefulness of the proposed distribution. It is shown that the TAD is more adequate for modeling this data than Aradhana distribution and some other available distributions.


Mohammed M. Gharaibeh




JJMS, 2020, 13(2), 287-304



Partition Dimension and Strong Metric Dimension of
Chain Cycle

Let G be a connected graph with vertex set V (G) and edge set E(G).
For an ordered k-partition Π = {Q1, . . . , Qk} of V (G), the representation of a vertex v ϵ V (G) with respect to Π is the k-vectors r(v|Π) = (d(v, Q1), . . . , d(v, Qk)), where d(v, Qi) is the distance between v and Qi . The partition Π is a resolving partition
if r(u|Π) ≠ r(v|Π), for each pair of distinct vertices u, v ϵ V (G). The minimum k for which there is a resolving k-partition of V (G) is the partition dimension of G.
A vertex w ϵ V (G) strongly resolves two distinct vertices u, v ϵ V (G) if u belongs to a shortest v − w path or v belongs to a shortest u − w path. An ordered set W = {w1, . . . , wt} ⊆ V (G) is a strong resolving set for G if for every two distinct vertices u and v of G there exists a vertex w ϵ W which strongly resolves u and v. A strong metric basis of G is a strong resolving set of minimal cardinality. The cardinality of a strong metric basis is called strong metric dimension of G. In this paper, we determine the partition dimension and strong metric dimension of a chain cycle constructed by even cycles and a chain cycle constructed by odd cycles.



Talmeez Ur Rehman
Naila Mehreen



JJMS, 2020, 13(2), 305-325