arXiv subjects

Igor Z. Milovanovic

Publications and source records attributed to Igor Z. Milovanovic.

3 recordsLinked to original sources

arXiv2023

Minimum Atom-Bond Sum-Connectivity Index of Trees With a Fixed Order and/or Number of Pendent Vertices

Let $d_u$ be the degree of a vertex $u$ of a graph $G$. The atom-bond sum-connectivity (ABS) index of a graph $G$ is the sum of the numbers $(1-2(d_v+d_w)^{-1})^{1/2}$ over all edges $vw$ of $G$. This paper gives the characterization of the graph possessing the minimum ABS index in the class of all trees of a fixed number of pendent vertices; the star is the unique extremal graph in the mentioned class of graphs. The problem of determining graphs possessing the minimum ABS index in the class of all trees with $n$ vertices and $p$ pendent vertices is also addressed; such extremal trees have the maximum degree $3$ when $n\ge 3p-2\ge7$, and the balanced double star is the unique such extremal tree for the case $p=n-2$.

math.CO↗

arXiv2023

On the Vertex-Degree-Function Indices of Connected (n,m)-Graphs of Maximum Degree at Most Four

Consider a graph $G$ and a real-valued function $f$ defined on the degree set of $G$. The sum of the outputs $f(d_v)$ over all vertices $v\in V(G)$ of $G$ is usually known as the vertex-degree-function indices and is denoted by $H_f(G)$, where $d_v$ represents the degree of a vertex $v$ of $G$. This paper gives sharp bounds on the index $H_f(G)$ in terms of order and size of $G$ when $G$ is connected and has the maximum degree at most $4$. All the graphs achieving the derived bounds are also determined. Bounds involving several existing indices - including the general zeroth-order Randić index and coindex, the general multiplicative first/second Zagreb index, the variable sum lodeg index, and the variable sum exdeg index - are deduced as the special cases of the obtained ones.

math.CO↗

arXiv2015

Remarks on Bounds of Normalized Laplacian Eigenvalues of Graphs

Let $G$ be a connected undirected graph with $n$, $n\ge 3$, vertices and $m$ edges. Denote by $ρ_1 \ge ρ_2 \ge \cdots > ρ_n =0$ the normalized Laplacian eigenvalues of $G$. Upper and lower bounds of $ρ_i$, $i=1,2,\ldots , n-1$, are determined in terms of $n$ and general Randi\' c index, $R_{-1}$.

math.SP↗