‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...

let g_1 and g_2 be simple connected graphs with disjoint vertex sets v(g_1) and v(g_2), respectively. for given vertices a_1in v(g_1) and a_2in v(g_2), a splice of g_1 and g_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the :union: of g_1 and g_2. in this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

This article studies a degree-bounded generalization of independent sets called co-k-plexes. Constant factor approximation algorithms are developed for the maximum co-k-plex problem on unit-disk graphs. The related problem of minimum co-k-plex coloring that generalizes classical vertex coloring is also studied in the context of unit-disk graphs. We extend several classical approximation results...

A metallaborane of novel structure, [(Cp*Mo)(2)B(3)H(3)Se(2){Fe(CO)(2)}(2){Fe(CO)(3)}(2)] (2; Cp* = η(5)-C(5)Me(5)), with tetracapped pentagonal bipyramidal geometry, isolated from the reaction of [(Cp*Mo)(2)B(4)H(4)Se(2)], 1 with [Fe(2)(CO)(9)]; the title compound exhibit an 11-vertex closo-cage geometry, having eight skeletal electron pairs (sep) and 98 valence electrons, appropriate for its ...

This paper offers a generalization of the independence polynomial, the co-k-plex polynomial. The resulting family of polynomials carries combinatorial information on a class of independence systems defined over the vertex set of a finite graph. Specifically, we offer a recursion formula and examples of the co-2-plex polynomial on certain graphs. In addition, we characterize the class of graphs ...

The vertex version of PI index is a molecular structure descriptor which is similar to vertex version of Szeged index. In this paper, we compute the vertex-PI index of TUC4C8(S), TUC4C8(R) and HAC5C7[r, p].

MOTIVATION Microarray-based gene expression data have been generated widely to study different biological processes and systems. Gene co-expression networks are often used to extract information about groups of genes that are 'functionally' related or co-regulated. However, the structural properties of such co-expression networks have not been rigorously studied and fully compared with known bi...

Abstract A topological descriptor is a mathematical illustration of molecular construction that relates particular physicochemical properties primary structure as well its depiction. Topological co-indices are usually applied for quantitative actions relationships (QSAR) and structures property (QSPR). descriptors which considered the noncontiguous vertex set. We study accompanying some renowne...