Jul 2026· ZERO Jurnal Sains Matematika dan Terapan· Vol 10, pp. 487· 0 citations· 29 references
Abstract
This study establishes exact formulas for the energy, Laplacian energy, and signless Laplacian energy of the lintang graph Ln and its line graph L(Ln). An algebraic spectral framework is employed to construct the associated matrices and determine their eigenvalues explicitly. In contrast to general results on line graph energies introduced by Ivan Gutman and subsequent studies, this work focuses on a specific two-hub graph structure for which explicit spectral formulas have not been previously reported. The results show that E(Ln) = 2 sqrt(2n), LE(L1) = QE(L1) = 10 sqrt(3), LE(Ln) = QE(Ln) = 4(n^2 - n + 2)/(n + 2) for n >= 2, and E(L(Ln)) = LE(L(Ln)) = QE(L(Ln)) = 4n - 4. These findings reveal a transition from sublinear to linear growth under the line graph transformation. The results contribute to spectral graph theory and are relevant to chemical graph theory and network analysis.
Graph energy is an important concept in spectral graph theory with applications in mathematics and chemistry. In this paper, we study the Laplacian minimum domination energy of derived graphs of some standard graphs. The main aim is to obtain formulas, properties, and bounds for this energy measure. The study considers...
Jagadeesh Rajanna, Ashwini Ankanahalli Shashidhara· American Journal of Applied...· 0 citations
In this research article, we replace the integer degree n = deg(v) of a vertex by its q(t)-analogue [n]q(t) and by an h(t)-analogue ⟨n⟩h(t) obtained from the h(t)-derivative of x n at x = 1, and we show that every classical degree-based index TI(G) = ∑︁uv∈E(G) F(deg u, deg v) admits two functional companions TIq(t)(G)...
Shrinath Manjarekar· Match-communications in Math...· 0 citations
We investigate wave solutions of the nonlinear Schrödinger equation (H-λ)u=f(x,u) on a locally finite weighted graph, where H is the associated Schrödinger operator. The central hypothesis is a tail summability condition 1/V∈l_m^1 (V) on the effective potential V, which, together with canonical compactifiability of the...
Setenay Akduman· Afyon Kocatepe University Jo...· 0 citations
An eigenvalue of the signless Laplacian $Q(G)$ is $Q$-main if its eigenspace is not orthogonal to the all-ones vector. We characterize graphs with exactly $\ell\ge3$ $Q$-main eigenvalues, one of which is zero. The case $\ell=3$ reduces to non-semiregular bipartite graphs satisfying a vertexwise signed degree-sum identi...
We study the heat content for Laplacians on compact, finite metric graphs with Dirichlet conditions imposed at the “boundary” (i.e., a given set of vertices) and standard conditions imposed elsewhere. We prove a closed formula of combinatorial flavor, as it is expressed as a sum over all paths starting and ending a...
Unknown authors· Annales de l'Institute Henri...· 0 citations
The reciprocal mean square (RMS) index of a graph G with edge set E(G) is defined by RMS(G)=∑uv∈E(G)[(d(u))2+(d(v))2]−1, where d(u) and d(v) are the degrees of vertices u and v, respectively. We first establish several bounds for the RMS index in terms of standard graph parameters (including the size, minimum degree, a...
A. Alotaibi, Akbar Ali· Mathematics· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
