In this paper, the distance and degree based topological indices for double silicate chain graph are obtained.

In this paper, we introduce a new form of fuzzy number named as Icosikaitetragonal fuzzy number with its membership function. It includes some basic arithmetic operations like addition, subtraction, multiplication and scalar multiplication by means of \(\alpha\)-cut with numerical illustrations.

In this paper, we determine the wirelength of embedding complete bipartite graphs \(K_{2^{n-1}, 2^{n-1}}\) into 1-rooted sibling tree \(ST_n^1\), and Cartesian product of 1-rooted sibling trees and paths.

A dominator coloring is a proper vertex coloring of a graph \(G\) such that each vertex is adjacent to all the vertices of at least one color class or either alone in its color class. The minimum cardinality among all dominator coloring of \(G\) is a dominator chromatic number of \(G\), denoted by \(X_d(G)\). On removal of a vertex the dominator chromatic number may increase or decrease or remain unaltered. In this paper, we have characterized nontrivial trees for which dominator chromatic number is stable.

If every induced sub graph \(H\) of a graph \(G\) contains a minimal dominating set that intersects every maximal cliques of \(H\), then \(G\) is SSP (super strongly perfect). This paper presents a cyclic structure of some circulant graphs and later investigates their SSP properties, while also giving attention to find the SSP parameters like colourability, cardinality of minimal dominating set and number of maximal cliques of circulant graphs.

A set \(S\) of vertices in a graph \(G\) is said to be a dominating set if every vertex in \(V(G)\S\) is adjacent to some vertex in \(S\). A dominating set \(S\) is called a total dominating set if each vertex of \(V(G)\) is adjacent to some vertex in \(S\). Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. In this pa-per, we determine the total domination number for certain nanotori using packing as a tool.

Among the varius coloring of graphs, the concept of equitable total coloring of graph \(G\) is the coloring of all its vertices and edges in which the number of elements in any two color classes differ by atmost one. The minimum number of colors required is called its equitable total chromatic number. In this paper, we obtained an equitable total chromatic number of middle graph of path, middle graph of cycle, total graph of path and total graph of cycle.

Making use of \(q\)-derivative operator, in this paper, we introduce new subclasses of the function class & of normalized analytic and bi-starlike functions defined in the open disk \(\mathbb{U}\). Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\). Moreover, we obtain Fekete-Szegö inequalities for the new function classes.

A set \(S\) of vertices in a graph \(G\) is called a dominating set of \(G\) if every vertex in \(V(G)\S\) is adjacent to some vertex in \(S\). A set S is said to be a power dominating set of \(G\) if every vertex in the system is monitored by the set \(S\) following a set of rules for power system monitoring. A zero forcing set of \(G\) is a subset of vertices B such that if the vertices in \(B\) are colored blue and the remaining vertices are colored white initially, repeated application of the color change rule can color all vertices of \(G\) blue. The power domination number and the zero forcing number of G are the minimum cardinality of a power dominating set and the minimum cardinality of a zero forcing set respectively of \(G\). In this paper, we obtain the power domination number, total power domination number, zero forcing number and total forcing number for m-rooted sibling trees, l-sibling trees and I-binary trees. We also solve power domination number for circular ladder, Möbius ladder, and extended cycle-of-ladder.

A proper vertex coloring of a graph where every node of the graph dominates all nodes of some color class is called the dominator coloring of the graph. The least number of colors used in the dominator coloring of a graph is called the dominator coloring number denoted by \(X_d(G)\). The dominator coloring number and domination number of central, middle, total and line graph of quadrilateral snake graph are derived and the relation between them are expressed in this paper.