Volume 5 Issue 6 by Mohammad Issa Sowaity
In this paper, we introduce the concept of the sum-eccentricity
matrix
S (G)
e
of a graph
G
and o... more In this paper, we introduce the concept of the sum-eccentricity
matrix
S (G)
e
of a graph
G
and obtain some coefficients of the characteristic
polynomial
P(G,)
of the sum-eccentricity matrix of
G
. We also introduce the
sum-eccentricity energy
ES (G)
e
of a graph
G
. Sum-eccentricity energies of
some well-known graphs are obtained. Upper and lower bounds for
ES (G)
e
are
estblished. It is shown that if the sum-eccentricity energy of a graph is
rational then it must be an even
Papers by Mohammad Issa Sowaity
TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 2020
Employee engagement is the buzz word in corporate circles. Where the boomers and millennials are ... more Employee engagement is the buzz word in corporate circles. Where the boomers and millennials are working together. In the wake of mass retrenchment and economic crises , there is a greater urgency for HR professionals to focus more attention on not only retaining this conglomerate work force, but also keeping them actively engaged .This paper focus on the initiative taken by IT industries in Mysore towards employee engagement.
Arab Journal of Basic and Applied Sciences, 2019
In this paper, we introduce the eccentric harmonic index H e ¼ H e ðGÞ of a graph G, so that it i... more In this paper, we introduce the eccentric harmonic index H e ¼ H e ðGÞ of a graph G, so that it is the sum of the terms 2 eiþej for the edges v i v j , where e i is the eccentricity of the i th vertex of the graph G. We compute the exact values of H e for some standard graphs. Bounds for H e are established. Relationships between H e and the eccentric connectivity index n c ðGÞ are derived.
Computers, Materials & Continua
In this article, we calculate various topological invariants such as symmetric division degree in... more In this article, we calculate various topological invariants such as symmetric division degree index, redefined Zagreb index, VL index, first and second exponential Zagreb index, first and second multiplicative exponential Zagreb indices, symmetric division degree entropy, redefined Zagreb entropy, VL entropy, first and second exponential Zagreb entropies, multiplicative exponential Zagreb entropy. We take the chemical compound named Proanthocyanidins, which is a very useful polyphenol in human's diet. They are very beneficial for one's health. These chemical compounds are extracted from grape seeds. They are tremendously anti-inflammatory. A subdivision form of this compound is presented in this article. The compound named subdivided grape seed Proanthocyanidins is abbreviated as SGSP 3. This network SGSP 3 , is converted and modeled into its mathematical graphical formation with the support of the latest mathematical tools. We have also developed many closed formulas for the measurement of entropy for the general chemical structure of the subdivided grape seed Proanthocyanidins network. The achieved outcomes can be correlated with the chemical version of SGSP 3 to get a better understanding of its biological as well as physical features.
The sum-eccentricity energy of a graph
In this paper, we introduce the concept of the sum-eccentricity matrix S (G) e of a graph G and o... more In this paper, we introduce the concept of the sum-eccentricity matrix S (G) e of a graph G and obtain some coefficients of the characteristic polynomial P(G, ) of the sum-eccentricity matrix of G . We also introduce the sum-eccentricity energy ES (G) e of a graph G . Sum-eccentricity energies of some well-known graphs are obtained. Upper and lower bounds for ES (G) e are estblished. It is shown that if the sum-eccentricity energy of a graph is rational then it must be an even.
We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-ecce... more We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=sum_{i=1}^n |eta_i|, where eta_i=zeta_i-frac{2m}{n} and where zeta_1,zeta_2,ldots,zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if sum_{i=1}^n |eta_i|=sum_{i=1}^n |zeta_i|. Conditions for the existence of such graphs are established.
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Volume 5 Issue 6 by Mohammad Issa Sowaity
matrix
S (G)
e
of a graph
G
and obtain some coefficients of the characteristic
polynomial
P(G,)
of the sum-eccentricity matrix of
G
. We also introduce the
sum-eccentricity energy
ES (G)
e
of a graph
G
. Sum-eccentricity energies of
some well-known graphs are obtained. Upper and lower bounds for
ES (G)
e
are
estblished. It is shown that if the sum-eccentricity energy of a graph is
rational then it must be an even
Papers by Mohammad Issa Sowaity
matrix
S (G)
e
of a graph
G
and obtain some coefficients of the characteristic
polynomial
P(G,)
of the sum-eccentricity matrix of
G
. We also introduce the
sum-eccentricity energy
ES (G)
e
of a graph
G
. Sum-eccentricity energies of
some well-known graphs are obtained. Upper and lower bounds for
ES (G)
e
are
estblished. It is shown that if the sum-eccentricity energy of a graph is
rational then it must be an even