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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Toufik Mansour
Department of Mathematics, University of Haifa, 3498838 Haifa, Israel
Electrical & Electronics Engineering

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Harary index of bipartite graphs Hanyuan Deng; Selvaraj Balachandran; Suresh Elumalai; Toufik Mansour
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2019.7.2.12

Abstract

Let G be a connected graph with vertex set V(G). The Harary index of a graph is defined as H(G) = ∑u ≠ v 1/d(u, v), where d(u, v) denotes the distance between u and v. In this paper, we determine the extremal graphs with the maximum Harary index among all bipartite graphs of order n with a given matching number, with a given vertex-connectivity and with a given edge-connectivity, respectively.
New bounds on the hyper-Zagreb index for the simple connected graphs Suresh Elumalai; Toufik Mansour; Mohammad Ali Rostami
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.1.12

Abstract

The hyper-Zagreb index of a simple connected graph G is defined by χ2(G) = ∑uv ∈ E(G)(d(u) + d(v))2. In this paper, we establish, analyze and compare some new upper bounds on the Hyper-Zagreb index in terms of the number of vertices n, number of edges m, maximum vertex degree Δ, and minimum vertex degree δ, first Zagreb index M1(G), second Zagreb index M2(G), harmonic index H(G), and inverse edge degree IED(G). In addition, we give the identities on Hyper-Zagreb index and its coindex for the simple connected graphs.
Log-concavity of the genus polynomials of Ringel Ladders Jonathan L Gross; Toufik Mansour; Thomas W. Tucker; David G.L. Wang
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 2 (2015): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2015.3.2.1

Abstract

A Ringel ladder can be formed by a self-bar-amalgamation operation on a symmetric ladder, that is, by joining the root vertices on its end-rungs. The present authors have previously derived criteria under which linear chains of copies of one or more graphs have log-concave genus polyno- mials. Herein we establish Ringel ladders as the first significant non-linear infinite family of graphs known to have log-concave genus polynomials. We construct an algebraic representation of self-bar-amalgamation as a matrix operation, to be applied to a vector representation of the partitioned genus distribution of a symmetric ladder. Analysis of the resulting genus polynomial involves the use of Chebyshev polynomials. This paper continues our quest to affirm the quarter-century-old conjecture that all graphs have log-concave genus polynomials.
Co-Authors David G.L. Wang Hanyuan Deng Jonathan L Gross Mohammad Ali Rostami Selvaraj Balachandran Suresh Elumalai Suresh Elumalai Thomas W. Tucker