On the variable sum exdeg index and cut edges of graphs

Authors

  • Adnan Aslam Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore (RCET), Pakistan
  • Ansa Kanwal Knowledge Unit of Science, University of Management and Technology, Sialkot, Pakistan
  • Bawfeh Kometa Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il, Saudi Arabia
  • Naveed Iqbal Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il, Saudi Arabia
  • Zahid Raza Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, UAE
Abstract:

The variable sum exdeg index of a graph G is defined as $SEI_a(G)=sum_{uin V(G)}d_G(u)a^{d_G(u)}$, where $aneq 1$ is a positive real number,  du(u) is the degree of a vertex u ∈ V (G). In this paper, we characterize the graphs with the extremum variable sum exdeg index among all the graphs having a fixed number of vertices and cut edges, for every a>1.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Bond Additive Modeling 5. Mathematical Properties of the Variable Sum Exdeg Index

Recently, discrete and variable Adriatic indices have been introduced and it has been shown that the sum α -exdeg index is good predictor (when variable parameter is equal to 0.37 ) of the octanol-water partition coefficient for octane isomers. Here, we study mathematical properties of this descriptor. Namely, we analyze extremal graphs of this descriptor in the following classes: the class of ...

full text

Ela on the Estrada Index of Graphs with given Number of Cut Edges

Let G be a simple graph with eigenvalues λ1, λ2, . . . , λn. The Estrada index of G is defined as EE(G) = ∑ n i=1 ei . In this paper, the unique graph with maximum Estrada index is determined among connected graphs with given numbers of vertices and cut edges.

full text

On the Estrada index of graphs with given number of cut edges

Let G be a simple graph with eigenvalues λ1, λ2, . . . , λn. The Estrada index of G is defined as EE(G) = ∑ n i=1 ei . In this paper, the unique graph with maximum Estrada index is determined among connected graphs with given numbers of vertices and cut edges.

full text

on the general sum–connectivity co–index of graphs

in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.

full text

On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

full text

On the spectral moment of graphs with k cut edges

Let A(G) be the adjacency matrix of a graph G with λ1(G), λ2(G), . . . , λn(G) its eigenvalues in non-increasing order. Call the number Sk(G) := ∑ n i=1 λ i (G) (k = 0, 1, . . . , n − 1) the kth spectral moment of G. Let S(G) = (S0(G), S1(G), . . . , Sn−1(G)) be the sequence of spectral moments of G. For two graphsG1 and G2, we have G1 ≺s G2 if Si(G1) = Si(G2) for i = 0, 1, . . . , k−1 and Sk(G...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 6  issue 2

pages  249- 257

publication date 2021-12-01

{@ msg @}

By following a journal you will be notified via email when a new issue of this journal is published.

Keywords

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023