It is well known that the G(n, p) model of random graphs undergoes a dramatic change around p = 1 n . It is here that the random graph, almost surely, contains cycles, and here it first acquires a giant (i.e., order Ω(n)) connected component. Several years ago, Linial and Meshulam introduced the Yd(n, p) model, a probability space of n-vertex d-dimensional simplicial complexes, where Y1(n, p) c...

In this paper, we determine the Randić energy of m-splitting graph, m-shadow graph and m-duplicate a given m being an arbitrary integer. Our results allow construction infinite sequence graphs having same energy. Further, some invariants like degree Kirchhoff index, Kemeny’s constant number spanning trees special graphs. From our results, indicate how to obtain infinitely many pairs equienerget...

Graph energy is defined to be the p -norm of adjacency matrix associated graph for = 1 elaborated as sum absolute eigenvalues matrix. The graph’s spectral radius represents matrix’s largest eigenvalue. Applications energies and radii can found in both molecular computing computer science. On similar lines, Inverse Sum Indeg, ( ISI ) energies, constructed. This article’s main focus generalized s...

A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if either ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 if ( ) ( ) f u f v , then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial ...

A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f∗ : E(G) → {1, 3, · · · , 2q − 1} defined by f∗(uv) = f(u) + f(v) is a bijection. A graph that admits odd harmonious labeling is called odd harmonious graph. In this paper, we prove that shadow and splitting of graph K2,n, Cn for n ≡ 0 (mod 4), the grap...

In this work some new odd graceful graphs are investigated. We prove that the graph obtained by fusing all the n vertices of Cn of even order with the apex vertices of n copies of K1,m admits odd graceful labeling. In addition to this we show that the shadow graphs of path Pn and star K1,n are odd graceful graphs.

Edge colorings of r-uniform hypergraphs naturally define a multicoloring on the 2-shadow, i.e. on the pairs that are covered by hyperedges. We show that in any (r− 1)-coloring of the edges of an r-uniform hypergraph with n vertices and at least (1−2)(n r ) edges, the 2-shadow has a monochromatic matching covering all but at most o(n) vertices. This result implies that for any fixed r and suffic...

Interval volumes are a generalization of isosurfaces that represent the set of points between two surfaces. In this paper, we present a compact multi-resolution representation for interval volume meshes extracted from regularly sampled volume data sets. The multi-resolution model is a hierarchical tetrahedral mesh whose updates are based on the longest edge bisection (LEB) subdivision strategy ...

A (p, q) graph G is said to be square sum, if there exists a bijection f : V (G) → {0, 1, 2, . . . , p − 1} such that the induced function f∗ : E(G)→ N defined by f∗(uv) = (f(u))2 + (f(v))2, for every uv ∈ E(G) is injective. In this paper we establish that if G is a square sum graph then G∪Pm is square sum, (Km,n) is square sum if and only if m+n ≤ 5 and W 2 n is square sum if and only if n ≤ 5...

Let G be an undirected graph with vertex and edge sets V (G) E(G), respectively. A set S ⊆ is called a hop independent dominating of if both G. The minimum cardinality G, denoted by γhih(G), the domination number In this paper, we show that lies between independence We characterize these types in shadow graph, join, corona, lexicographic product two graphs. Moreover, either exact values or boun...