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New types of integral sum graphs
2003
Discrete Mathematics
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In this paper we enlarge the types of integral sum graphs. We prove that some caterpillars and mPn are integral sum graphs and some conjectures of Harary are wrong. ...
Harary (Discrete Math. 124(1-3) (1994) 99) introduced the intergral sum graphs, and proved that the path Pn and matching mK2 are integer sum graphs, and o ered some conjectures. ...
Acknowledgements The authors wish to thank the referee for useful comments and suggestions that have allowed them to improve the presentation of this paper. ...
doi:10.1016/s0012-365x(02)00456-9
fatcat:kyge6z3szjb7lkxtjc2y3o6cue
Page 7570 of Mathematical Reviews Vol. , Issue 98M
[page]
1998
Mathematical Reviews
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In the present paper the author first introduces some methods of identification for constructing new connected integral sum graphs from given integral sum graphs. ...
The idea of integral sum graphs was introduced by F. Harary [Discrete Math. 124 (1994), no. 1-3, 99-105; MR 95b:05202]. ...
Page 3605 of Mathematical Reviews Vol. , Issue 94f
[page]
1994
Mathematical Reviews
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Metric invariants, named topological indices in chemical literature, such as the graph- distance index (the total sum of all distances in the graph G), the eccentricity index (the sum of eccentricies of ...
vertices in G), the graph chain-distance index (the sum of chain-distances in G) and the chain-eccentricity index (the sum of chain-eccentricities of vertices in G) are defined. ...
Page 187 of Physical Review Vol. 94, Issue 1
[page]
1954
Physical Review
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When the summation over all graphs is made, there occur a set of graphs all of which have the same reduced integral and the same type of subpart (vertex or self- energy), but in the set this part appears ...
they cancel exactly with similar terms from the P brackets in the S matrix.®
The new field variables ¥,*, ¥:, and A; are operators which annihilate and create a new type of bare particles which have not ...
Page 8955 of Mathematical Reviews Vol. , Issue 2003m
[page]
2003
Mathematical Reviews
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8955
The integral sum graph G*(S) is defined just as the sum graph, the difference being that S Cc Z instead of SCN, Z= {...,—-3, —2,—1,0,1,2,3,...}. ...
Harary [Discrete Math. 124 (1994), no. 1-3, 99-105; MR 95b:05202] has pointed out that, for each positive integer n, the path P,, and matching nK> are integral sum graphs. ...
A Combinatorial Interpretation of the Integral of the Product of Legendre Polynomials
1988
SIAM Journal on Mathematical Analysis
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In addition, a number of apparently new combinatorial identities are obtained. ...
k, not all of which seem analytically straightforward, including a direct combinatorial derivation of the known formula for Ia,b, and the expression of Ia,b,c,d as a simple finite sum. ...
It remains to determine how many such graphs there are. Consider (12). Since there are B edges of type 1 3 in the graph, this will also be the number of segments of type (ii). ...
doi:10.1137/0519109
fatcat:adackwudanf63p6vka34vh2gta
Macdonald Polynomials and Chromatic Quasisymmetric Functions
2020
Electronic Journal of Combinatorics
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We express the integral form Macdonald polynomials as a weighted sum of Shareshian and Wachs' chromatic quasisymmetric functions of certain graphs. ...
Then we use known expansions of these chromatic quasisymmetric functions into Schur and power sum symmetric functions to provide Schur and power sum formulas for the integral form Macdonald polynomials ...
We let IFT µ denote the collection of all integral form tableaux of type µ (of varying shapes λ). is an integral form tableau of type (2, 2, 2) and shape (3, 2, 1). ...
doi:10.37236/9011
fatcat:i227miog6bgsppbut24y62k57e
Integral sum graphs from identification
1998
Discrete Mathematics
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In this paper, we first introduce some methods of identification on constructing new connected integral sum graphs from given integral sum graphs. ...
The idea of integral sum graphs was introduced by Harary (1994) . ...
In the present paper, we shall present some methods on constructing new connected integral sum graphs from given integral sum graphs by identification. ...
doi:10.1016/s0012-365x(97)00046-0
fatcat:rsliaguf75fcxiyxqsxlz4vcuq
Page 531 of Physical Review Vol. 88, Issue 3
[page]
1952
Physical Review
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Any ¢ may be replaced by a contribution in- volving a vertex of type (0’), yielding a new graph which must be considered in the enumeration. ...
Letting A[@o ] be the contribution to the energy arising from graphs in 2’, the condition that the sum of all contributions from subgraphs of type (8) vanishes is then expressed by the equation
5A[ Go ...
Automatic integration of digital system requirements using schemata
[chapter]
1995
Lecture Notes in Computer Science
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This paper describes a rule-based algorithm for the integration of requirements which are expressed as conceptual graphs. ...
Natural language and diagrams of various types are commonly used for specifications on digital systems containing descriptions and requirements. ...
Whenever the integrator comes across a new concept type in the requirement graph it searches the database for a schema for the concept type. ...
doi:10.1007/3-540-60161-9_28
fatcat:eikwnhxgj5atthhbksgveo32ke
The ne plus ultra of tree graph inequalities
1990
Letters in Mathematical Physics
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of the interaction, and integration by parts. ...
This includes applications to both two-body and many-body potential situations of the recently obtained 'new improved tree graph inequalities" that have led to the 'extra I/N! factors'. ...
by a sum of terms of similar type. ...
doi:10.1007/bf00429953
fatcat:w3kvljp475fy7kruhk74wlnxqu
Running Nonlocal Lagrangians
[article]
1992
arXiv
pre-print
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In a scalar field theory, we write an integro-differential renormalization group equation for every possible class of graph at one loop order. ...
We investigate the renormalization of "nonlocal" interactions in an effective field theory using dimensional regularization with minimal subtraction. ...
Hence the resummation of the pole terms for a sum starting at zero gives a higher dimensional angular integral.
2m-point function of type n at one loop For the non-trivial general graph with n ≥ 2, after ...
arXiv:hep-ph/9205242v1
fatcat:6rek54zprnbyldzk4nt4uf4g2y
Macdonald polynomials and chromatic quasisymmetric functions
[article]
2018
arXiv
pre-print
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Other Versions
We express the integral form Macdonald polynomials as a weighted sum of Shareshian and Wachs' chromatic quasisymmetric functions of certain graphs. ...
Then we use known expansions of these chromatic quasisymmetric functions into Schur and power sum symmetric functions to provide Schur and power sum formulas for the integral form Macdonald polynomials ...
First, we define a new weight function on integral form tableaux. To compute wt J (α) µ ′ (x) = T ∈IFTµ wt (α) µ (T )s shape(T ) (54) where the sum is over all integral form tableaux of type µ. ...
arXiv:1701.05622v2
fatcat:cdexduugmvfjtp6zqnirlrt36a
RenormalizedS-Matrix for Scalar Electrodynamics
1952
Physical Review
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new type of “vertex,” illustrated in Fig. 5 with the vertex factor 2ip, since [—1/2mi(0/0p,)Dr=Dr-2ip,: Dy» |. ...
Yy»* similarly denotes the sum of integrals for all graphs with only the first and the last end-vertices unchanged 4-vertices, and Z,»* the sum for graphs with only the first end-vertex an unchanged 4- ...
doi:10.1103/physrev.86.731
fatcat:usl4zpaybverhg6vfztu4kea64
Page 612 of Physical Review Vol. 83, Issue 3
[page]
1951
Physical Review
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Now, whenever Y; has one of the last four forms (58), the corresponding vertex x; is of a new type, having two photon lines and no electron line incident. ...
The coefficient M is a sum of contributions Mz from the various terms in the sum (55). ...
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