• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.793-807
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• 2012

If G is any connected graph of order p; then the thorn graph $G_p^*$ with code ($n_1$, $n_2$, ${\cdots}$, $n_p$) is obtained by adding $n_i$ pendent vertices to each $i^{th}$ vertex of G. By treating the pendent edge of a thorn graph as $P_2$, $K_2$, $K_{1,1}$, $K_1{\circ}K_1$ or $P_1{\circ}K_1$, we generalize a thorn graph by replacing $P_2$ by $P_m$, $K_2$ by $K_m$, $K_{1,1}$ by $K_{m,n}$, $K_1{\circ}K_1$ by $K_m{\circ}K_1$ and $P_1{\circ}K_1$ by $P_m{\circ}K_1$ and their respective generalized thorn graphs are denoted by $G_P$, $G_K$, $G_B$, $G_{KK}$ and $G_{PK}$ respectively. Many chemical compounds can be treated as $G_P$, $G_K$, $G_B$, $G_{KK}$ and $G_{PK}$ of some graphs in graph theory. In this paper, we obtain the bounds of the wiener index for these generalization of thorn graphs.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.9-17
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• 2016

In this paper, it has been shown that the hairy cycle C_n ⊙ rK₁, n ≡ 3(mod4), the graph obtained by adding pendant edge to each pendant vertex of hairy cycle C_n ⊙ 1K₁, n ≡ 0(mod4), double graph of path P_n and double graph of comb P_n ⊙ 1K₁ are k-graceful.

• Journal of Korea Multimedia Society
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• v.6 no.3
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• pp.556-564
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• 2003

A Star and Pancake graph also have such a good property of a hypercube and have a low network cost than the hypercube. A Macro-star graph which has the star graph as a basic module has the node symmetry, the maximum fault tolerance, and the hierarchical decomposition property. And, it is an interconnection network which improves the network cost against the Star graph. In this paper, we propose a method to embed between Star graph, Pancake graph, and Macro-star graph using the edge definition of graphs. We prove that the Star graph $S_n$ can be embedded into Pancake graph $P_n$ with dilation 4, and Macro-star graph MS(2,n) can be embedded into Pancake graph $P_{2n＋1}$ with dilation 4. Also, we have a result that the embedding cost, a Pancake graph can be embedded into Star and Macro-star graph, is O(n).

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.159-167
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• 2024

The Topological indices are known as Mathematical characterization of molecules. In this paper, we have studied line graph of subdivision and semi-total point graph of triangular benzenoid, polynomino chains of 8-cycles and graphene sheet through forgotten and first Zagreb indices.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.769-776
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• 2010

A pebbling move on a connected graph G is taking two pebbles off of one vertex and placing one of them on an adjacent vertex. For a connected graph G, $G^p$ (p > 1) is the graph obtained from G by adding the edges (u, v) to G whenever 2 $\leq$ dist(u, v) $\leq$ p in G. And the pebbling exponent of a graph G to be the least power of p such that the pebbling number of $G^p$ is equal to the number of vertices of G. We compute the pebbling number of fourth power of paths so that the pebbling exponents of some paths are calculated.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1193-1207
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• 2023

In this paper, we introduce an iP₂ extension of a star graph S_n for n ≥ 2 and 1 ≤ i ≤ n - 1. Certain general properties satisfied by order, size, domination (or Roman) numbers γ (or γ_R) of an iP₂ extended star graph are studied. Finally, we study how the parameters such as chromatic number and harmonious chromatic number are affected when an iP₂ extension process acts on the star graphs.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1051-1060
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• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.241-257
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• 2013

An automorphism group of a graph is said to be $s$-regular if it acts regularly on the set of $s$-arcs in the graph. A graph is $s$-regular if its full automorphism group is $s$-regular. In the present paper, all $s$-regular cubic graphs of order $10p^3$ are classified for each $s{\geq}1$ and each prime $p$.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.197-201
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• 2014

In this paper, we study some properties of finite or infinite poset P determined by properties of the ideal based zero-divisor graph properties $G_J(P)$, for an ideal J of P.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1137-1145
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• 1996

A Steinhaus graph is a labelled graph whose adjacency matrix $A = (a_{i,j})$ has the Steinhaus property : $a_{i,j} + a{i,j+1} \equiv a_{i+1,j+1} (mod 2)$. We consider random Steinhaus graphs with n labelled vertices in which edges are chosen independently and with probability $\frac{1}{2}$. We prove that almost all Steinhaus graphs are Hamiltonian like as in random graph theory.