An (a, d)-edge-antimagic total labeling of a graph G with p vertices and q edges is a bijection f from the set of all vertices and edges to the set of positive integers {1, 2, 3, . . . , p + q} such that all the edge-weights w(uv) = f(u) + f(v) + f(uv);uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edgeantimagic total labeling is called a sup...

Algebraic combinatorics is the area of mathematics that uses the theories and methods of abstract and linear algebra to solve combinatorial problems, or conversely applies combinatorial techniques to solve problems in algebra. In particular, spectral graph theory applies the techniques of linear algebra to study graph theory. Spectral graph theory is the study of the eigenvalues of various matr...

Let n be any positive integer and Fn be the friendship (or Dutch windmill) graph with 2n+1 vertices and 3n edges. Here we study graphs with the same adjacency spectrum as Fn. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let G be a graph cospectral with Fn. Here we prove that if G has no cycle of length 4 or 5, then G ∼= Fn. Moreover if G...

In this paper, we introduce the E-Banhatti Sombor index and modified their corresponding exponentials of a graph. Also compute these newly defined indices for wheel graphs, friendship tetrameric 1,3-adamantane honeycomb networks. Furthermore, establish some properties index.

Topological indices (molecular descriptors) are numerical values of a chemical structure and represented by graph. Molecular descriptors used in QSPR/QSAR modeling to determine structure’s physical, biological, properties. The cycle graphs symmetric for any number vertices. In this paper, recently defined neighborhood degree sum-based molecular polynomials studied. NM-polynomials some cycle-rel...

The friendship paradox is a sociological phenomenon stating that most people have fewer friends than their friends do. The generalized friendship paradox refers to the same observation for attributes other than degree, and it has been observed in Twitter and scientific collaboration networks. This paper takes an analytical approach to model this phenomenon. We consider a preferential attachment...

A new graph invariant called the secure vertex cover pebbling number, which is a combination of two invariants, namely, ‘secure cover’ and ‘cover number’, introduced in this paper. The number graph, [Formula: see text], minimum text] so that every distribution pebbles can reach some by sequence moves. In paper, complexity problem are discussed. Also, we obtain basic results for complete text]-p...

Antimagic labeling of a graph with vertices and edges is assigned the labels for its by some integers from set , such that no two received same label, weights are pairwise distinct. Where vertex-weights vertex under this sum all incident to vertex, in paper, we deal problem finding antimagic edge special families graphs called strong face graphs. We prove antimagic, ladder wheel fan prism final...