Minimum degree polynomial of graphs obtained by some graph operators

Abstract

The minimum degree matrix MD(G) of a graph G of order n is an n × n symmetric matrix whose (i, j) th entry is min{d i , d j } whenever i = j, and zero otherwise, where d i and d j are the degrees of the i th and j th vertices of G, respectively. In the present work, we obtain the minimum degree polynomial of the graphs obtained by some graph operators (generalized xyz-point-line transformation graphs).

On Maximum Degree and Maximum Reverse Degree Energies of Splitting and Shadow graph of Complete graph

“…[5] establishes relations between the maximum energy and minimum energy of the shadow and splitting graphs of a graph. In [6], the characteristic polynomial of the minimum degree matrix of graphs obtained by certain graph operations is discussed, along with bounds for the largest minimum degree eigenvalue and minimum degree energy of graphs. [7] provides the energy of a graph class in terms of another graph class after removing a vertex.…”

Topological indices and QSPR modeling of some novel drugs used in the cancer treatment

“…Many polynomials have been defined to overcome this issue [7–11]. One of them is the M‐polynomial for the TIs that depend on the degree [12–17]. Another is NM‐polynomials that depend on the sum of adjacent vertex degrees [18,19].…”

M-Polynomial of Generalized Transformation Graphs B. Basavanagoud and Goutam Veerapur

“…Where m ij , i, j ≥ 1, is the number of edges uv of G such that {d G (u)), d G (v)} = {i, j} [11]. Recently, the study of M − polynomial are reported in [9,16,17,18,6,4,3].…”