Abstract: A graph G with p vertices is said to be strongly multiplicative if the vertices of G can be labeled with p consecutive positive integers 1, 2, ..., p such that label induced on the edges by the product of labels of end vertices are all distinct. In this paper we investigate strongly multiplicative labeling of some snake related graphs. We prove that alternate triangular snake and alte...

Let ( , ) G V E be a simple graph. For a total labeling { } : 1,2,3,..., V E k ∂ ∪ → the weight of a vertex x is defined as ( ) ( ) ( ). xy E wt x x xy ∈ = ∂ + ∂ ∑ ∂ is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y, ( ) ( ). wt x wt y ≠ . The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularit...

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

In this paper, we consider the problem of exploring unknown environments with autonomous agents. We model the environment as a graph with edge weights and analyze the task of visiting all vertices of the graph at least once. The hardness of this task heavily depends on the knowledge and the capabilities of the agent. In our model, the agent sees the whole graph in advance, but does not know the...

As the extension of the previous work by Ciucu and the present authors (J. Combin. Theory Ser. A 112(2005) 105–116), this paper considers the problem of enumeration of spanning trees of weighted graphs with an involution which allows fixed points. We show that if G is a weighted graph with an involution, then the sum of weights of spanning trees of G can be expressed in terms of the product of ...

The q− difference analog of the classical ladder operators is derived for those orthogonal polynomials arising from a class of indeterminate moments problem.

In this paper, by way of three examples – a fourth order low pass active RC filter, a rudimentary BJT amplifier, and an LC ladder – we show, how the algebraic capabilities of modern computer algebra systems can, or in the last example, might be brought to use in the task of designing analog circuits. ACM Classification: I.1 Symbolic and algebraic manipulation; J.2 Physical sciences and engineer...

Let A be an abelian group. An A-magic of a graph G = (V, E) is a labeling f : E(G) → A\{0} such that the sum of the labels of the edges incident with u ∈ V is a constant, where 0 is the identity element of the group A. In this paper we prove Z3-magic labeling for the class of even cycles, Bistar, ladder, biregular graphs and for a certain class of Cayley digraphs. Mathematics Subject Classifica...

In the title compound, C29H24N2O2, the hydrofuran ring is twisted with puckering parameters Q = 0.1553 (16) Å and ϕ = 305.0 (6)°. In the crystal, the graph-set motifs of the inter-action pattern are an R2(2)(16) motif involving dimers through N-H⋯N hydrogen bonds across centres of inversion and a C(6) motif through C-H⋯O hydrogen-bond between glide-related mol-ecules. Together, these generate [...

We consider first-passage percolation on a ladder, i.e. the graph N × {0, 1} where nodes at distance 1 are joined by an edge, and the times are exponentially i.i.d. with mean 1. We find an appropriate Markov chain to calculate an explicit expression for the time constant whose numerical value is ≈ 0.6827. This time constant is the long-term average inverse speed of the process.